Browsing by Author "Rashid, Saima"

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Citation Count: Rashid, Saima;...et.al. (2022). "A comprehensive analysis of the stochastic fractal–fractional tuberculosis model via Mittag-Leffler kernel and white noise", Results in Physics, Vol.39.
A comprehensive analysis of the stochastic fractal–fractional tuberculosis model via Mittag-Leffler kernel and white noise
(2022) Rashid, Saima; Iqbal, Muhammad Kashif; Alshehri, Ahmed M.; Ashraf, Rehana; Jarad, Fahd; 234808
In this research, we develop a stochastic framework for analysing tuberculosis (TB) evolution that includes newborn immunization via the fractal–fractional (F–F) derivative in the Atangana–Baleanu sense. The population is divided into four groups by this system: susceptibility S(ξ), infectious I(ξ), immunized infants V(ξ), and restored R(ξ). The stochastic technique is used to describe and assess the invariant region, basic reproduction number, and local stability for disease-free equilibrium. This strategy has significant modelling difficulties since it ignores the unpredictability of the system phenomena. To prevent such problems, we convert the deterministic strategy to a randomized one, which seems recognized to have a vital influence by adding an element of authenticity and fractional approach. Owing to the model intricacies, we established the existence-uniqueness of the model and the extinction of infection was carried out. We conducted a number of experimental tests using the F–F derivative approach and obtained some intriguing modelling findings in terms of (i) varying fractional-order (φ) and fixing fractal-dimension (ω), (ii) varying ω and fixing φ, and (iii) varying both φ and ω, indicating that a combination of such a scheme can enhance infant vaccination and adequate intervention of infectious patients can give a significant boost.
Citation Count: Al Qurashi, Maysaa; Rashid, Saima; Jarad, Fahd. (2022). "A computational study of a stochastic fractal-fractional hepatitis B virus infection incorporating delayed immune reactions via the exponential decay", Mathematical Biosciences and Engineering, Vol.19, No.12, pp.12950-12980.
A computational study of a stochastic fractal-fractional hepatitis B virus infection incorporating delayed immune reactions via the exponential decay
(2022) Al Qurashi, Maysaa; Rashid, Saima; Jarad, Fahd; 234808
Recently, researchers have become interested in modelling, monitoring, and treatment of hepatitis B virus infection. Understanding the various connections between pathogens, immune systems, and general liver function is crucial. In this study, we propose a higher-order stochastically modified delay differential model for the evolution of hepatitis B virus transmission involving defensive cells. Taking into account environmental stimuli and ambiguities, we presented numerical solutions of the fractal-fractional hepatitis B virus model based on the exponential decay kernel that reviewed the hepatitis B virus immune system involving cytotoxic T lymphocyte immunological mechanisms. Furthermore, qualitative aspects of the system are analyzed such as the existence-uniqueness of the non-negative solution, where the infection endures stochastically as a result of the solution evolving within the predetermined system’s equilibrium state. In certain settings, infection-free can be determined, where the illness settles down tremendously with unit probability. To predict the viability of the fractal-fractional derivative outcomes, a novel numerical approach is used, resulting in several remarkable modelling results, including a change in fractional-order δ with constant fractal-dimension $, δ with changing $, and δ with changing both δ and $. White noise concentration has a significant impact on how bacterial infections are treated.
Citation Count: Rashid, Saima...et al. (2020). "A New Dynamic Scheme via Fractional Operators on Time Scale", Frontiers in Physics, Vol. 8.
A New Dynamic Scheme via Fractional Operators on Time Scale
(2020) Rashid, Saima; Noor, Muhammad Aslam; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Rahman, Gauhar; 56389
The present work investigates the applicability and effectiveness of the generalized Riemann-Liouville fractional integral operator integral method to obtain new Minkowski, Gruss type and several other associated dynamic variants on an arbitrary time scale, which are communicated as a combination of delta and fractional integrals. These inequalities extend some dynamic variants on time scales, and tie together and expand some integral inequalities. The present method is efficient, reliable, and it can be used as an alternative to establishing new solutions for different types of fractional differential equations applied in mathematical physics.
Citation Count: Rashid, Saima; Jarad, Fahd; Chu, Yu-Ming (2020). "A Note on Reverse Minkowski Inequality via Generalized Proportional Fractional Integral Operator with respect to Another Function", Mathematical Problems in Engineering, Vol. 2020.
A Note on Reverse Minkowski Inequality via Generalized Proportional Fractional Integral Operator with respect to Another Function
(2020) Rashid, Saima; Jarad, Fahd; Chu, Yu-Ming; 234808
This study reveals new fractional behavior of Minkowski inequality and several other related generalizations in the frame of the newly proposed fractional operators. For this, an efficient technique called generalized proportional fractional integral operator with respect to another function phi is introduced. This strategy usually arises as a description of the exponential functions in their kernels in terms of another function phi. The prime purpose of this study is to provide a new fractional technique, which need not use small parameters for finding the approximate solution of fractional coupled systems and eliminate linearization and unrealistic factors. Numerical results represent that the proposed technique is efficient, reliable, and easy to use for a large variety of physical systems. This study shows that a more general proportional fractional operator is very accurate and effective for analysis of the nonlinear behavior of boundary value problems. This study also states that our findings are more convenient and efficient than other available results.
Citation Count: Alqurashi, M.S.;...et.al. (2022). "A novel formulation of the fuzzy hybrid transform for dealing nonlinear partial differential equations via fuzzy fractional derivative involving general order", AIMS Mathematics, Vol.7, No.8, pp.14946-14974.
A novel formulation of the fuzzy hybrid transform for dealing nonlinear partial differential equations via fuzzy fractional derivative involving general order
(2022) Alqurashi, M.S.; Rashid, Saima; Kanwal, Bushra; Jarad, Fahd; Elagan, S.K.; 234808
The main objective of the investigation is to broaden the description of Caputo fractional derivatives (in short, CFDs) (of order 0 < α < r) considering all relevant permutations of entities involving t1 equal to 1 and t2 (the others) equal to 2 via fuzzifications. Under gH-differentiability, we also construct fuzzy Elzaki transforms for CFDs for the generic fractional order α ∈ (r − 1, r). Furthermore, a novel decomposition method for obtaining the solutions to nonlinear fuzzy fractional partial differential equations (PDEs) via the fuzzy Elzaki transform is constructed. The aforesaid scheme is a novel correlation of the fuzzy Elzaki transform and the Adomian decomposition method. In terms of CFD, several new results for the general fractional order are obtained via gH-differentiability. By considering the triangular fuzzy numbers of a nonlinear fuzzy fractional PDE, the correctness and capabilities of the proposed algorithm are demonstrated. In the domain of fractional sense, the schematic representation and tabulated outcomes indicate that the algorithm technique is precise and straightforward. Subsequently, future directions and concluding remarks are acted upon with the most focused use of references.
Citation Count: Rashid, Saima; Jarad, Fahd; Ahmad, Abdulaziz G. (2022). "A novel fractal-fractional order model for the understanding of an oscillatory and complex behavior of human liver with non-singular kernel", Results in Physics, Vol.35.
A novel fractal-fractional order model for the understanding of an oscillatory and complex behavior of human liver with non-singular kernel
(2022) Rashid, Saima; Jarad, Fahd; Ahmad, Abdulaziz Garba; 234808
Scientists and researchers are increasingly interested in numerical simulations of infections with non-integer orders. It is self-evident that conventional epidemiological systems can be given in a predetermined order, but fractional-order derivative systems are not stable orders. The fractional derivative proves increasingly effective in representing real-world issues when it has a non-fixed order. Various novel fractional operator notions, including special functions in the kernel, have been presented in recent decades, which transcend the constraints of prior fractional order derivatives. These novel operators have been shown to be useful in simulating scientific and technical challenges. The fractal-fractional operator is a relatively modern fractional calculus operator that has been proposed. Besides that, we propose a new technique and implement it in a human liver model and want to investigate its dynamics. In the context of this novel operator, we demonstrate certain interesting findings for the human liver model. The findings of the uniqueness and existence will be revealed. We describe modeling estimates for the proposed model using an innovative numerical method that has never been used before for a human liver model of this type. Additionally, graphical illustrations are demonstrated for both fractal and fractional orders. It is expected that the fractal-fractional approach is more invigorating and effective for epidemic models than the fractional operator.
Citation Count: Rashid, Saima...et.al. (2022). "A novel numerical dynamics of fractional derivatives involving singular and nonsingular kernels: designing a stochastic cholera epidemic model", Aims Mathematics, Vol.8, No. 2, pp. 3484-3522.
A novel numerical dynamics of fractional derivatives involving singular and nonsingular kernels: designing a stochastic cholera epidemic model
(2022) Rashid, Saima; Jarad, Fahd; Alsubaie, Hajid; Aly, Ayman A.; Alotaibi, Ahmed; 234808
In this research, we investigate the direct interaction acquisition method to create a stochastic computational formula of cholera infection evolution via the fractional calculus theory. Susceptible people, infected individuals, medicated individuals, and restored individuals are all included in the framework. Besides that, we transformed the mathematical approach into a stochastic model since it neglected the randomization mechanism and external influences. The descriptive behaviours of systems are then investigated, including the global positivity of the solution, ergodicity and stationary distribution are carried out. Furthermore, the stochastic reproductive number for the system is determined while for the case Rs0 > 1, some sufficient condition for the existence of stationary distribution is obtained. To test the complexity of the proposed scheme, various fractional derivative operators such as power law, exponential decay law and the generalized Mittag-Leffler kernel were used. We included a stochastic factor in every case and employed linear growth and Lipschitz criteria to illustrate the existence and uniqueness of solutions. So every case was numerically investigated, utilizing the newest numerical technique. According to simulation data, the main significant aspects of eradicating cholera infection from society are reduced interaction incidence, improved therapeutic rate, and hygiene facilities.
Citation Count: Rashid, Saima;...et.al. (2022). "A peculiar application of the fractal–fractional derivative in the dynamics of a nonlinear scabies model", Results in Physics, Vol.38.
A peculiar application of the fractal–fractional derivative in the dynamics of a nonlinear scabies model
(2022) Rashid, Saima; Kanwal, Bushra; Jarad, Fahd; Elagan, S.K.; 234808
In this paper, we provide a generic mathematical framework for scabies transmission mechanisms. The infections involving susceptible, highly contagious people and juvenile scabiei mites are characterized by a framework of ordinary differential equations (DEs). The objective of this study is to examine the evolution of scabies disease employing a revolutionary configuration termed a fractal–fractional (FF) Atangana–Baleanu (AB) operator. Generic dynamical estimates are used to simulate the underlying pace of growth of vulnerable people, clinical outcomes, and also the eradication and propagation rates of contaminated people and immature mites. We study and comprehend our system, focusing on a variety of restrictions on its basic functionalities. The model's outcomes are assessed for positivity and boundedness. The formula includes a fundamental reproducing factor, R0, that ensures the presence and stability of all relevant states. Furthermore, the FF-AB operator is employed in the scabies model, and its mathematical formulation is presented using a novel process. We analyze the FF framework to construct various fractal and fractional levels and conclude that the FF theory predicts the affected occurrences of scabies illness adequately. The relevance and usefulness of the recently described operator has been demonstrated through simulations of various patterns of fractal and fractional data.
Citation Count: Rashid, Saima; Jarad, Fahd; Jawa, Taghreed M. (2022). "A study of behaviour for fractional order diabetes model via the nonsingular Kernel", AIMS Mathematics, Vol.7, No.4, pp.5072-5092.
A study of behaviour for fractional order diabetes model via the nonsingular Kernel
(2022) Rashid, Saima; Jarad, Fahd; Jawa, Taghreed M.; 234808
A susceptible diabetes comorbidity model was used in the mathematical treatment to explain the predominance of mellitus. In the susceptible diabetes comorbidity model, diabetic patients were divided into three groups: susceptible diabetes, uncomplicated diabetics, and complicated diabetics. In this research, we investigate the susceptible diabetes comorbidity model and its intricacy via the Atangana-Baleanu fractional derivative operator in the Caputo sense (ABC). The analysis backs up the idea that the aforesaid fractional order technique plays an important role in predicting whether or not a person will develop diabetes after a substantial immunological assault. Using the fixed point postulates, several theoretic outcomes of existence and Ulam’s stability are proposed for the susceptible diabetes comorbidity model. Meanwhile, a mathematical approach is provided for determining the numerical solution of the developed framework employing the Adams type predictor–corrector algorithm for the ABC-fractional integral operator. Numerous mathematical representations correlating to multiple fractional orders are shown. It brings up the prospect of employing this structure to generate framework regulators for glucose metabolism in type 2 diabetes mellitus patients.
Citation Count: Al-Qurashi, Maysaa...et al. (2021). "ACHIEVING MORE PRECISE BOUNDS BASED ON DOUBLE AND TRIPLE INTEGRAL AS PROPOSED BY GENERALIZED PROPORTIONAL FRACTIONAL OPERATORS IN THE HILFER SENSE", Fractals-Complex Geometry Patterns and Scaling in Nature and Society, Vol. 29, No. 05.
ACHIEVING MORE PRECISE BOUNDS BASED ON DOUBLE AND TRIPLE INTEGRAL AS PROPOSED BY GENERALIZED PROPORTIONAL FRACTIONAL OPERATORS IN THE HILFER SENSE
(2021) Al-Qurashi, Maysaa; Rashid, Saima; Karaca, Yeliz; Hammouch, Zakia; Baleanu, Dumitru; Chu, Yu-Ming; 56389
A user-friendly approach depending on nonlocal kernel has been constituted in this study to model nonlocal behaviors of fractional differential and difference equations, which is known as a generalized proportional fractional operator in the Hilfer sense. It is deemed, for differentiable functions, by a fractional integral operator applied to the derivative of a function having an exponential function in the kernel. This operator generalizes a novel version of Cebysev-type inequality in two and three variables sense and furthers the result of existing literature as a particular case of the Cebysev inequality is discussed. Some novel special cases are also apprehended and compared with existing results. The outcome obtained by this study is very broad in nature and fits in terms of yielding an enormous number of relating results simply by practicing the proportionality indices included therein. Furthermore, the outcome of our study demonstrates that the proposed plans are of significant importance and computationally appealing to deal with comparable sorts of differential equations. Taken together, the results can serve as efficient and robust means for the purpose of investigating specific classes of integrodifferential equations.
Citation Count: Al-Qurashi, Maysaa...et.al. (2023). "Dynamic prediction modelling and equilibrium stability of a fractional discrete biophysical neuron model", Results in Physics, Vol.48.
Dynamic prediction modelling and equilibrium stability of a fractional discrete biophysical neuron model
(2023) Al-Qurashi, Maysaa; Rashid, Saima; Jarad, Fahd; Ali, Elsiddeg; Egami, Ria H.; 234808
Here, we contemplate discrete-time fractional-order neural connectivity using the discrete nabla operator. Taking into account significant advances in the analysis of discrete fractional calculus, as well as the assertion that the complexities of discrete-time neural networks in fractional-order contexts have not yet been adequately reported. Considering a dynamic fast–slow FitzHugh–Rinzel (FHR) framework for elliptic eruptions with a fixed number of features and a consistent power flow to identify such behavioural traits. In an attempt to determine the effect of a biological neuron, the extension of this integer-order framework offers a variety of neurogenesis reactions (frequent spiking, swift diluting, erupting, blended vibrations, etc.). It is still unclear exactly how much the fractional-order complexities may alter the fring attributes of excitatory structures. We investigate how the implosion of the integer-order reaction varies with perturbation, with predictability and bifurcation interpretation dependent on the fractional-order β∈(0,1]. The memory kernel of the fractional-order interactions is responsible for this. Despite the fact that an initial impulse delay is present, the fractional-order FHR framework has a lower fring incidence than the integer-order approximation. We also look at the responses of associated FHR receptors that synchronize at distinctive fractional orders and have weak interfacial expertise. This fractional-order structure can be formed to exhibit a variety of neurocomputational functionalities, thanks to its intriguing transient properties, which strengthen the responsive neurogenesis structures.
Citation Count: Al-Qureshi, Maysaa;...et.al. "Dynamical behavior of a stochastic highly pathogenic avian influenza A (HPAI) epidemic model via piecewise fractional differential technique", AIMS Mathematics, Vol8, No.1, pp.1737-1756.
Dynamical behavior of a stochastic highly pathogenic avian influenza A (HPAI) epidemic model via piecewise fractional differential technique
(2023) Al-Qureshi, Maysaa; Rashid, Saima; Jarad, Fahd; Alharthi, Mohammed Shaaf; 234808
In this research, we investigate the dynamical behaviour of a HPAI epidemic system featuring a half-saturated transmission rate and significant evidence of crossover behaviours. Although simulations have proposed numerous mathematical frameworks to portray these behaviours, it is evident that their mathematical representations cannot adequately describe the crossover behaviours, particularly the change from deterministic reboots to stochastics. Furthermore, we show that the stochastic process has a threshold number Rs0 that can predict pathogen extermination and mean persistence. Furthermore, we show that if Rs0 > 1, an ergodic stationary distribution corresponds to the stochastic version of the aforementioned system by constructing a sequence of appropriate Lyapunov candidates. The fractional framework is expanded to the piecewise approach, and a simulation tool for interactive representation is provided. We present several illustrated findings for the system that demonstrate the utility of the piecewise estimation technique. The acquired findings offer no uncertainty that this notion is a revolutionary viewpoint that will assist mankind in identifying nature.
Citation Count: Zhou, Shuang-Shuang...et al. (2021). "Efficient computations for weighted generalized proportional fractional operators with respect to a monotone function", AIMS Mathematics, Vol. 6, no. 8, pp. 8001-8029.
Efficient computations for weighted generalized proportional fractional operators with respect to a monotone function
(2021) Zhou, Shuang-Shuang; Rashid, Saima; Rauf, Asia; Jarad, Fahd; Hamed, Y. S.; Abualnaja, Khadijah M.; 234808
In this paper, we propose a new framework of weighted generalized proportional fractional integral operator with respect to a monotone function psi; we develop novel modifications of the aforesaid operator. Moreover, contemplating the so-called operator, we determine several notable weighted Chebyshev and Gruss type inequalities with respect to increasing, positive and monotone functions psi by employing traditional and forthright inequalities. Furthermore, we demonstrate the applications of the new operator with numerous integral inequalities by inducing assumptions on ! and psi verified the superiority of the suggested scheme in terms of e fficiency. Additionally, our consequences have a potential association with the previous results. The computations of the proposed scheme show that the approach is straightforward to apply and computationally very user-friendly and accurate.
Citation Count: Al Qurashi, Maysaa;...et.al. (2022). "Fractional-order partial differential equations describing propagation of shallow water waves depending on power and Mittag-Leffler memory", AIMS Mathematics, Vol.7, No.7, pp. 12587-12619.
Fractional-order partial differential equations describing propagation of shallow water waves depending on power and Mittag-Leffler memory
(2022) Al Qurashi, Maysaa; Rashid, Saima; Sultana, Sobia; Jarad, Fahd; Alsharif, Abdullah M.; 234808
In this research, the ¯q-homotopy analysis transform method (¯q-HATM) is employed to identify fractional-order Whitham–Broer–Kaup equation (WBKE) solutions. The WBKE is extensively employed to examine tsunami waves. With the aid of Caputo and Atangana-Baleanu fractional derivative operators, to obtain the analytical findings of WBKE, the predicted algorithm employs a combination of ¯q-HAM and the Aboodh transform. The fractional operators are applied in this work to show how important they are in generalizing the frameworks connected with kernels of singularity and non-singularity. To demonstrate the applicability of the suggested methodology, various relevant problems are solved. Graphical and tabular results are used to display and assess the findings of the suggested approach. In addition, the findings of our recommended approach were analyzed in relation to existing methods. The projected approach has fewer processing requirements and a better accuracy rate. Ultimately, the obtained results reveal that the improved strategy is both trustworthy and meticulous when it comes to assessing the influence of nonlinear systems of both integer and fractional order.
Citation Count: Rashid, Saima;...et.al. (2022). "Fuzzy fractional estimates of Swift-Hohenberg model obtained using the Atangana-Baleanu fractional derivative operator", AIMS Mathematics, Vol.7, No.9, pp.16067-16101.
Fuzzy fractional estimates of Swift-Hohenberg model obtained using the Atangana-Baleanu fractional derivative operator
(2022) Rashid, Saima; Sultana, Sobia; Kanwal, Bushra; Jarad, Fahd; Khalid, Aasma; 234808
Swift-Hohenberg equations are frequently used to model the biological, physical and chemical processes that lead to pattern generation, and they can realistically represent the findings. This study evaluates the Elzaki Adomian decomposition method (EADM), which integrates a semi-analytical approach using a novel hybridized fuzzy integral transform and the Adomian decomposition method. Moreover, we employ this strategy to address the fractional-order Swift-Hohenberg model (SHM) assuming gH-differentiability by utilizing different initial requirements. The Elzaki transform is used to illustrate certain characteristics of the fuzzy Atangana-Baleanu operator in the Caputo framework. Furthermore, we determined the generic framework and analytical solutions by successfully testing cases in the series form of the systems under consideration. Using the synthesized strategy, we construct the approximate outcomes of the SHM with visualizations of the initial value issues by incorporating the fuzzy factor ϖ ∈ [0, 1] which encompasses the varying fractional values. Finally, the EADM is predicted to be effective and precise in generating the analytical results for dynamical fuzzy fractional partial differential equations that emerge in scientific disciplines.
Citation Count: Khan, Zareen A...et al. (2020). "Generalized trapezium-type inequalities in the settings of fractal sets for functions having generalized convexity property", Advances in Difference Equations, Vol. 2020, No. 1.
Generalized trapezium-type inequalities in the settings of fractal sets for functions having generalized convexity property
(2020) Khan, Zareen A.; Rashid, Saima; Ashraf, Rehana; Baleanu, Dumitru; Chu, Yu-Ming; 56389
In the paper, we extend some previous results dealing with the Hermite–Hadamard inequalities with fractal sets and several auxiliary results that vary with local fractional derivatives introduced in the recent literature. We provide new generalizations for the third-order differentiability by employing the local fractional technique for functions whose local fractional derivatives in the absolute values are generalized convex and obtain several bounds and new results applicable to convex functions by using the generalized Hölder and power-mean inequalities. As an application, numerous novel cases can be obtained from our outcomes. To ensure the feasibility of the proposed method, we present two examples to verify the method. It should be pointed out that the investigation of our findings in fractal analysis and inequality theory is vital to our perception of the real world since they are more realistic models of natural and man-made phenomena. © 2020, The Author(s).
Citation Count: Rashid, Saima...et al. (2020). "Generation of new fractional inequalities via n polynomials s-type convexity with applications", Advances in Difference Equations, Vol. 2020, No. 1.
Generation of new fractional inequalities via n polynomials s-type convexity with applications
(2020) Rashid, Saima; Iscan, Imdat; Baleanu, Dumitru; Chu, Yu-Ming; 56389
The celebrated Hermite-Hadamard and Ostrowski type inequalities have been studied extensively since they have been established. We find novel versions of the Hermite-Hadamard and Ostrowski type inequalities for the n-polynomial s-type convex functions in the frame of fractional calculus. Taking into account the new concept, we derive some generalizations that capture novel results under investigation. We present two different general techniques, for the functions whose first and second derivatives in absolute value at certain powers are n-polynomial s-type convex functions by employing K-fractional integral operators have yielded intriguing results. Applications and motivations of presented results are briefly discussed that generate novel variants related to quadrature rules that will be helpful for in-depth investigation in fractal theory, optimization and machine learning.
Citation Count: Rashid, Saima...et.al. (2023). "Global dynamics of deterministic-stochastic dengue infection model including multi specific receptors via crossover effects", AIMS Mathematics, Vol.8, No.3, pp.6466-6503.
Global dynamics of deterministic-stochastic dengue infection model including multi specific receptors via crossover effects
(2023) Rashid, Saima; Jarad, Fahd; El-Marouf, Sobhy A. A.; Elagan, Sayed K.; 234808
Dengue viruses have distinct viral regularities due to the their serotypes. Dengue can be aggravated from a simple fever in an acute infection to a presumably fatal secondary pathogen. This article investigates a deterministic-stochastic secondary dengue viral infection (SDVI) model including logistic growth and a nonlinear incidence rate through the use of piecewise fractional differential equations. This framework accounts for the fact that the dengue virus can penetrate various kinds of specific receptors. Because of the supplementary infection, the system comprises both heterologous and homologous antibody. For the deterministic case, we determine the invariant region and threshold for the aforesaid model. Besides that, we demonstrate that the suggested stochastic SDVI model yields a global and non-negative solution. Taking into consideration effective Lyapunov candidates, the sufficient requirements for the presence of an ergodic stationary distribution of the solution to the stochastic SDVI model are generated. This report basically utilizes a novel idea of piecewise differentiation and integration. This method aids in the acquisition of mechanisms, including crossover impacts. Graphical illustrations of piecewise modeling techniques for chaos challenges are demonstrated. A piecewise numerical scheme is addressed. For various cases, numerical simulations are presented.
Citation Count: Rashid, Saima; Jarad, Fahd; Noor, Muhammad Aslam (2020). "Grüss-type integrals inequalities via generalized proportional fractional operators", Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, Vol. 114, No. 2.
Grüss-type integrals inequalities via generalized proportional fractional operators
(2020) Rashid, Saima; Jarad, Fahd; Noor, Muhammad Aslam; 234808
In the article, we deal with the generalized proportional fractional integral, establish several kinds of inequalities such as Grüss-type and certain other inequalities by use of generalized proportional fractional integral. Moreover, several special cases are discussed. Also, we derive certain particular results by utilizing the connection between generalized proportional fractional integral and Riemann–Liouville integral. Furthermore, an illustrative example is presented to support our outcomes. © 2020, The Royal Academy of Sciences, Madrid.
Citation Count: Al-Qurashi, Maysaa;...ET.AL. (2023). "Identification of numerical solutions of a fractal-fractional divorce epidemic model of nonlinear systems via anti-divorce counseling", AIMS Mathematics,
Identification of numerical solutions of a fractal-fractional divorce epidemic model of nonlinear systems via anti-divorce counseling
(2023) Al-Qurashi, Maysaa; Sultana, Sobia; Karim, Shazia; Rashid, Saima; Jarad, Fahd; Alharthi, Mohammed Shaaf; 234808
Divorce is the dissolution of two parties’ marriage. Separation and divorce are the major obstacles to the viability of a stable family dynamic. In this research, we employ a basic incidence functional as the source of interpersonal disagreement to build an epidemiological framework of divorce outbreaks via the fractal-fractional technique in the Atangana-Baleanu perspective. The research utilized Lyapunov processes to determine whether the two steady states (divorce-free and endemic steady state point) are globally asymptotically robust. Local stability and eigenvalues methodologies were used to examine local stability. The next-generation matrix approach also provides the fundamental reproducing quantity R¯0 . The existence and stability of the equilibrium point can be assessed using ¯R0, demonstrating that counseling services for the separated are beneficial to the individuals’ well-being and, as a result, the population. The fractal-fractional Atangana-Baleanu operator is applied to the divorce epidemic model, and an innovative technique is used to illustrate its mathematical interpretation. We compare the fractal-fractional model to a framework accommodating different fractal-dimensions and fractional-orders and deduce that the fractal-fractional data fits the stabilized marriages significantly and cannot break again.