Browsing by Author "Rashid, Saima"

Now showing 1 - 20 of 63

Citation - WoS: 17
Citation - Scopus: 19
Achieving More Precise Bounds Based on Double and Triple Integral as Proposed by Generalized Proportional Fractional Operators in the Hilfer Sense
(World Scientific Publ Co Pte Ltd, 2021) Rashid, Saima; Karaca, Yeliz; Hammouch, Zakia; Baleanu, Dumitru; Chu, Yu-Ming; Al-Qurashi, Maysaa; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 19
Citation - Scopus: 21
A Comprehensive Analysis of the Stochastic Fractal-Fractional Tuberculosis Model Via Mittag-Leffler Kernel and White Noise
(Elsevier, 2022) Iqbal, Muhammad Kashif; Alshehri, Ahmed M.; Ashraf, Rehana; Jarad, Fahd; Rashid, Saima; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this research, we develop a stochastic framework for analysing tuberculosis (TB) evolution that includes new-born 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(xi), infectious I(xi), immunized infants V(xi), and restored R(xi). 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 (phi) and fixing fractal-dimension (omega), (ii) varying omega and fixing phi, and (iii) varying both phi and omega, indicating that a combination of such a scheme can enhance infant vaccination and adequate intervention of infectious patients can give a significant boost.
Citation - WoS: 12
Citation - Scopus: 11
A Computational Study of a Stochastic Fractal-Fractional Hepatitis B Virus Infection Incorporating Delayed Immune Reactions Via the Exponential Decay
(Amer inst Mathematical Sciences-aims, 2022) Rashid, Saima; Jarad, Fahd; Al Qurashi, Maysaa; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 delta with constant fractal-dimension pi, delta with changing pi, and delta with changing both delta and pi. White noise concentration has a significant impact on how bacterial infections are treated.
Citation - WoS: 15
Citation - Scopus: 17
Dynamic Prediction Modelling and Equilibrium Stability of a Fractional Discrete Biophysical Neuron Model
(Elsevier, 2023) Rashid, Saima; Jarad, Fahd; Ali, Elsiddeg; Egami, Ria H.; Al-Qurashi, Maysaa; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 �� & ISIN; (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 - WoS: 12
Citation - Scopus: 12
Dynamical Behavior of a Stochastic Highly Pathogenic Avian Influenza a (Hpai) Epidemic Model Via Piecewise Fractional Differential Technique
(Amer inst Mathematical Sciences-aims, 2022) Rashid, Saima; Jarad, Fahd; Alharthi, Mohammed Shaaf; Al-Qureshi, Maysaa; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 R-0(S) that can predict pathogen extermination and mean persistence. Furthermore, we show that if R-0(S) > 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 - WoS: 14
Citation - Scopus: 13
Efficient Computations for Weighted Generalized Proportional Fractional Operators With Respect To a Monotone Function
(Amer inst Mathematical Sciences-aims, 2021) Rashid, Saima; Rauf, Asia; Jarad, Fahd; Hamed, Y. S.; Abualnaja, Khadijah M.; Zhou, Shuang-Shuang; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 6
Citation - Scopus: 7
Fixed Point Results of a New Family of Hybrid Contractions in Generalised Metric Space With Applications
(Amer inst Mathematical Sciences-aims, 2022) Jiddah, Jamilu Abubakar; Noorwali, Maha; Shagari, Mohammed Shehu; Rashid, Saima; Jarad, Fahd; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this manuscript, a novel general family of contraction, called hybrid-interpolative ReichIstrat,escu-type (G-alpha-mu)-contraction is introduced and some fixed point results in generalised metric space that are not deducible from their akin in metric spaces are obtained. The preeminence of this class of contraction is that its contractive inequality can be extended in a variety of manners, depending on the given parameters. Consequently, a number of corollaries that reduce our result to other wellknown results in the literature are highlighted and analysed. Substantial examples are constructed to validate the assumptions of our obtained theorems and to show their distinction from corresponding results. Additionally, one of our obtained corollaries is applied to set up unprecedented existence conditions for solution of a family of integral equations.
Citation - WoS: 8
Citation - Scopus: 10
Fractional-Order Partial Differential Equations Describing Propagation of Shallow Water Waves Depending on Power and Mittag-Leffier Memory
(Amer inst Mathematical Sciences-aims, 2022) Rashid, Saima; Sultana, Sobia; Jarad, Fahd; Alsharif, Abdullah M.; Al Qurashi, Maysaa; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this research, the (q) over bar -homotopy analysis transform method ((q) over bar -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) over bar -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 - WoS: 3
Citation - Scopus: 3
Fuzzy Fractional Estimates of Swift-Hohenberg Model Obtained Using the Atangana-Baleanu Fractional Derivative Operator
(Amer inst Mathematical Sciences-aims, 2022) Sultana, Sobia; Kanwal, Bushra; Jarad, Fahd; Khalid, Aasma; Rashid, Saima; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 pi is an element of [0, 1] which encompasses the varying fractional values. Finally, the EADM is predicted to be e ffective and precise in generating the analytical results for dynamical fuzzy fractional partial di fferential equations that emerge in scientific disciplines.
Citation - WoS: 30
Citation - Scopus: 26
Generalized Trapezium-Type Inequalities in the Settings of Fractal Sets for Functions Having Generalized Convexity Property
(Springer, 2020) Ashraf, Rehana; Rashid, Saima; Baleanu, Dumitru; Chu, Yu-Ming; Khan, Zareen A.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 Holder 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.
Citation - WoS: 67
Citation - Scopus: 87
Generation of New Fractional Inequalities Via N Polynomials S-Type Convexity With Applications
(Springer, 2020) Iscan, Imdat; Baleanu, Dumitru; Chu, Yu-Ming; Rashid, Saima; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 13
Citation - Scopus: 13
Global Dynamics of Deterministic-Stochastic Dengue Infection Model Including Multi Specific Receptors Via Crossover Effects
(Amer inst Mathematical Sciences-aims, 2023) Jarad, Fahd; El-Marouf, Sobhy A. A.; Elagan, Sayed K.; Rashid, Saima; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 15
Citation - Scopus: 19
Gruss-Type Integrals Inequalities Via Generalized Proportional Fractional Operators
(Springer-verlag Italia Srl, 2020) Jarad, Fahd; Noor, Muhammad Aslam; Rashid, Saima; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In the article, we deal with the generalized proportional fractional integral, establish several kinds of inequalities such as Gruss-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.
Citation - WoS: 3
Citation - Scopus: 3
Identification of Numerical Solutions of a Fractal-Fractional Divorce Epidemic Model of Nonlinear Systems Via Anti-Divorce Counseling
(Amer inst Mathematical Sciences-aims, 2023) Sultana, Sobia; Karim, Shazia; Rashid, Saima; Jarad, Fahd; Alharthi, Mohammed Shaaf; Al-Qurashi, Maysaa; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 over bar R0. The existence and stability of the equilibrium point can be assessed using R over bar 0, 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.
Citation - WoS: 86
Citation - Scopus: 107
Inequalities by Means of Generalized Proportional Fractional Integral Operators With Respect To Another Function
(Mdpi, 2019) Jarad, Fahd; Noor, Muhammad Aslam; Kalsoom, Humaira; Chu, Yu-Ming; Rashid, Saima; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this article, we define a new fractional technique which is known as generalized proportional fractional (GPF) integral in the sense of another function Psi. The authors prove several inequalities for newly defined GPF-integral with respect to another function Psi. Our consequences will give noted outcomes for a suitable variation to the GPF-integral in the sense of another function Psi and the proportionality index sigma. Furthermore, we present the application of the novel operator with several integral inequalities. A few new properties are exhibited, and the numerical approximation of these new operators is introduced with certain utilities to real-world problems.
Citation - WoS: 7
Citation - Scopus: 7
Interpolative Contractions and Intuitionistic Fuzzy Set-Valued Maps With Applications
(Amer inst Mathematical Sciences-aims, 2022) Rashid, Saima; Jarad, Fahd; Mohamed, Mohamed S.; Shagari, Mohammed Shehu; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Over time, the interpolative approach in fixed point theory (FPT) has been investigated only in the setting of crisp mathematics, thereby dropping-off a significant amount of useful results. As an attempt to fill up the aforementioned gaps, this paper initiates certain hybrid concepts under the names of interpolative Hardy-Rogers-type (IHRT) and interpolative Reich-Rus-Ciric type (IRRCT) intuitionistic fuzzy contractions in the frame of metric space (MS). Adequate criteria for the existence of intuitionistic fuzzy fixed point (FP) for such contractions are examined. On the basis that FP of a single-valued mapping obeying interpolative type contractive inequality is not always unique, and thereby making the ideas more suitable for FP theorems of multi-valued mappings, a few special cases regarding point-to-point and non-fuzzy set-valued mappings which include the conclusions of some well-known results in the corresponding literature are highlighted and discussed. In addition, comparative examples which dwell on the generality of our obtained results are constructed.
Citation - WoS: 9
Citation - Scopus: 9
More Efficient Estimates Via H-Discrete Fractional Calculus Theory and Applications
(Pergamon-elsevier Science Ltd, 2021) Sultana, Sobia; Jarad, Fahd; Jafari, Hossein; Hamed, Y. S.; Rashid, Saima; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Discrete fractional calculus (DFC) is continuously spreading in the engineering practice, neural networks, chaotic maps, and image encryption, which is appropriately assumed for discrete-time modelling in continuum problems. First, we start with a novel discrete h-proportional fractional sum defined on the time scale hZ so as to give the premise to the more broad and complex structures, for example, the suitably accustomed transformations conjuring the property of observing the new chaotic behaviors of the logistic map. Here, we aim to present the novel discrete versions of Gruss and certain other associated variants by employing discrete h-proportional fractional sums are established. Moreover, several novel consequences are recaptured by the h-discrete fractional sums. The present study deals with the modification of Young, weighted-arithmetic and geometric mean formula by taking into account changes in the exponential function in the kernel represented by the parameters of the operator, varying delivery noted outcomes. In addition, two illustrative examples are apprehended to demonstrate the applicability and efficiency of the proposed technique. (C) 2021 Elsevier Ltd. All rights reserved.
Citation - WoS: 12
Citation - Scopus: 12
More New Results on Integral Inequalities for Generalized K-Fractional Conformable Integral Operators
(Amer inst Mathematical Sciences-aims, 2021) Rashid, Saima; Jarad, Fahd; Noor, Muhammad Aslam; Kalsoom, Humaira; Chu, Yu-Ming; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This paper aims to investigate the several generalizations by newly proposed generalized K-fractional conformable integral operator. Based on these novel ideas, we derived a novel framework to study for Cebysev and Polya-Szego type inequalities by generalized K-fractional conformable integral operator. Several special cases are apprehended in the light of generalized fractional conformable integral. This novel strategy captures several existing results in the relative literature. We also aim at showing important connections of the results here with those including Riemann-Liouville fractional integral operator.
Citation - WoS: 74
Citation - Scopus: 84
More Properties of the Proportional Fractional Integrals and Derivatives of a Function With Respect To Another Function
(Springer, 2020) Rashid, Saima; Hammouch, Zakia; Jarad, Fahd; Abdeljawad, Thabet; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this article, we present some new properties of the fractional proportional derivatives of a function with respect to a certain function. We use a modified Laplace transform to find the relation between the derivatives in the Riemann-Liouville setting and the one in Caputo. In addition, we provide an integration by parts formulas related to the considered operators.
New (p, q)-estimates for different types of integral inequalities via (alpha, m)-convex mappings
(2020) Kalsoom, Humaira; Latif, Muhammad Amer; Rashid, Saima; Baleanu, Dumitru; Chu, Yu-Ming; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In the article, we present a new (p, q)-integral identity for the first-order (p, q)-differentiable functions and establish several new (p, q)-quantum error estimations for various integral inequalities via (a alpha, m)-convexity. We also compare our results with the previously known results and provide two examples to show the superiority of our obtained results.p>