Browsing by Author "Rashid, Saima"

Now showing 1 - 20 of 63

Citation - WoS: 23
Citation - Scopus: 26
New Newton's Type Estimates Pertaining To Local Fractional Integral Via Generalized P-Convexity With Applications
(World Scientific Publ Co Pte Ltd, 2021) Rashid, Saima; Hammouch, Zakia; Baleanu, Dumitru; Chu, Yu-ming; LI, Yong-min
This paper aims to investigate the notion of p-convex functions on fractal sets Double-struck capital R-alpha(0 < alpha <= 1). Based on these novel ideas, we derived an auxiliary result depend on a three-step quadratic kernel by employing generalized p-convexity. Take into account the local fractal identity, we established novel Newton's type variants for the local differentiable functions. Several special cases are apprehended in the light of generalized convex functions and generalized harmonically convex functions. This novel strategy captures several existing results in the relative literature. Application is obtained in cumulative distribution function and generalized special weighted means to confirm the relevance and computational effectiveness of the considered method. Finally, we supposed that the consequences of this paper can stimulate those who are interested in fractal analysis.
New (p, q)-estimates for different types of integral inequalities via (α, m)-convex mappings
(2020) Kalsoom, Humaira; Latif, Muhammad Amer; Rashid, Saima; Baleanu, Dumitru; Chu, Yu-Ming
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 (α, m)-convexity. We also compare our results with the previously known results and provide two examples to show the superiority of our obtained results.
Citation - WoS: 14
Citation - Scopus: 18
Strong Interaction of Jafari Decomposition Method With Nonlinear Fractional-Order Partial Differential Equations Arising in Plasma Via the Singular and Nonsingular Kernels
(Amer inst Mathematical Sciences-aims, 2022) Ashraf, Rehana; Jarad, Fahd; Rashid, Saima
This research utilizes the Jafari transform and the Adomian decomposition method to derive a fascinating explicit pattern for the outcomes of the KdV, mKdV, K(2,2) and K(3,3) models that involve the Caputo fractional derivative operator and the Atangana-Baleanu fractional derivative operator in the Caputo sense. The novel exact-approximate solutions are derived from the formulation of trigonometric, hyperbolic, and exponential function forms. Laser and plasma sciences may benefit from these solutions. It is demonstrated that this approach produces a simple and effective mathematical framework for tackling nonlinear problems. To provide additional context for these ideas, simulations are performed, employing a computationally packaged program to assist in comprehending the implications of solutions.
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
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: 7
Citation - Scopus: 6
Novel Stochastic Dynamics of a Fractal-Fractional Immune Effector Response To Viral Infection Via Latently Infectious Tissues
(Amer inst Mathematical Sciences-aims, 2022) Ashraf, Rehana; Asif, Qurat-Ul-Ain; Jarad, Fahd; Rashid, Saima
In this paper, the global complexities of a stochastic virus transmission framework featuring adaptive response and Holling type II estimation are examined via the non-local fractal-fractional derivative operator in the Atangana-Baleanu perspective. Furthermore, we determine the existenceuniqueness of positivity of the appropriate solutions. Ergodicity and stationary distribution of nonnegative solutions are carried out. Besides that, the infection progresses in the sense of randomization as a consequence of the response fluctuating within the predictive case's equilibria. Additionally, the extinction criteria have been established. To understand the reliability of the findings, simulation studies utilizing the fractal-fractional dynamics of the synthesized trajectory under the Atangana-BaleanuCaputo derivative incorporating fractional-order alpha and fractal-dimension P have also been addressed. The strength of white noise is significant in the treatment of viral pathogens. The persistence of a stationary distribution can be maintained by white noise of sufficient concentration, whereas the eradication of the infection is aided by white noise of high concentration.
Citation - WoS: 10
Citation - Scopus: 11
New Insights for the Fuzzy Fractional Partial Differential Equations Pertaining To Katugampola Generalized Hukuhara Differentiability in the Frame of Caputo Operator and Fixed Point Technique
(Elsevier, 2024) Jarad, Fahd; Alamri, Hind; Rashid, Saima
In this article, we use the Caputo-Katugampola gH-differentiability to solve a class of fractional PDE systems. With the aid of Caputo-Katugampola gH-differentiability, we demonstrate the existence and uniqueness outcomes of two types of gH-weak findings of the framework of fuzzy fractional coupled PDEs using Lipschitz assumptions and employing the Banach fixed point theorem with the mathematical induction technique. Moreover, owing to the entanglement in the initial value problems (IVPs), we establish the p Gronwall inequality of the matrix pattern and inventively explain the continuous dependence of the coupled framework's responses on the given assumptions and the epsilon-approximate solution of the coupled system. An illustrative example is provided to demonstrate that their existence and unique outcomes are accurate. Through experimentation, we demonstrate the efficacy of the suggested approach in resolving fractional differential equation algorithms under conditions of uncertainty found in engineering and physical phenomena. Additionally, comparisons are drawn for the computed outcomes. Ultimately, we make several suggestions for futuristic work.
Citation - WoS: 26
Citation - Scopus: 29
A Novel Fractal-Fractional Order Model for the Understanding of an Oscillatory and Complex Behavior of Human Liver With Non-Singular Kernel
(Elsevier, 2022) Jarad, Fahd; Ahmad, Abdulaziz Garba; Rashid, Saima
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 - WoS: 21
Citation - Scopus: 23
Some New Extensions for Fractional Integral Operator Having Exponential in the Kernel and Their Applications in Physical Systems
(de Gruyter Poland Sp Z O O, 2020) Baleanu, Dumitru; Chu, Yu-Ming; Rashid, Saima
The key purpose of this study is to suggest a new fractional extension of Hermite-Hadamard, Hermite-Hadamard-Fejer and Pachpatte-type inequalities for harmonically convex functions with exponential in the kernel. Taking into account the new operator, we derived some generalizations that capture novel results under investigation with the aid of the fractional operators. We presented, in general, two different techniques that can be used to solve some new generalizations of increasing functions with the assumption of convexity by employing more general fractional integral operators having exponential in the kernel have yielded intriguing results. The results achieved by the use of the suggested scheme unfold that the used computational outcomes are very accurate, flexible, effective and simple to perform to examine the future research in circuit theory and complex waveforms.
Citation - WoS: 17
Citation - Scopus: 19
New Numerical Dynamics of the Fractional Monkeypox Virus Model Transmission Pertaining To Nonsingular Kernels
(Amer inst Mathematical Sciences-aims, 2023) Rashid, Saima; Alshehri, Ahmed M.; Jarad, Fahd; Safdar, Farhat; Al Qurashi, Maysaa
Monkeypox (MPX) is a zoonotic illness that is analogous to smallpox. Monkeypox infections have moved across the forests of Central Africa, where they were first discovered, to other parts of the world. It is transmitted by the monkeypox virus, which is a member of the Poxviridae species and belongs to the Orthopoxvirus genus. In this article, the monkeypox virus is investigated using a deterministic mathematical framework within the Atangana-Baleanu fractional derivative that depends on the generalized Mittag-Leffler (GML) kernel. The system's equilibrium conditions are investigated and examined for robustness. The global stability of the endemic equilibrium is addressed using Jacobian matrix techniques and the Routh-Hurwitz threshold. Furthermore, we also identify a criterion wherein the system's disease-free equilibrium is globally asymptotically stable. Also, we employ a new approach by combining the two-step Lagrange polynomial and the fundamental concept of fractional calculus. The numerical simulations for multiple fractional orders reveal that as the fractional order reduces from 1, the virus's transmission declines. The analysis results show that the proposed strategy is successful at reducing the number of occurrences in multiple groups. It is evident that the findings suggest that isolating affected people from the general community can assist in limiting the transmission of pathogens.
NEW MULTI-FUNCTIONAL APPROACH for κ TH-ORDER DIFFERENTIABILITY GOVERNED by FRACTIONAL CALCULUS VIA APPROXIMATELY GENERALIZED (ψ, ?) -CONVEX FUNCTIONS in HILBERT SPACE
(2021) Wang, Miao-Kun; Rashid, Saima; Karaca, Yeliz; Baleanu, Dumitru; Chu, Yu-Ming
This work addresses several novel classes of convex function involving arbitrary non-negative function, which is known as approximately generalized (ψ, ?)-convex and approximately ψ-quasiconvex function, with respect to Raina's function, which are elaborated in Hilbert space. To ensure the feasibility of the proposed concept and with the discussion of special cases, it is presented that these classes generate other classes of generalized (ψ, ?)-convex functions such as higher-order strongly (HOS) generalized (ψ, ?)-convex functions and HOS generalized ψ-quasiconvex function. The core of the proposed method is a newly developed Simpson's type of identity in the settings of Riemann-Liouville fractional integral operator. Based on the HOS generalized (ψ, ?)-convex function representation, we established several theorems and related novel consequences. The presented results demonstrate better performance for HOS generalized ψ-quasiconvex functions where we can generate several other novel classes for convex functions that exist in the relative literature. Accordingly, the assortment in this study aims at presenting a direction in the related fields. © 2021 The Author(s).
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
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: 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
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: 86
Citation - Scopus: 108
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
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: 24
Citation - Scopus: 19
Quantum Analogs of Ostrowski-Type Inequalities for Raina's Function Correlated With Coordinated Generalized Φ-Convex Functions
(Mdpi, 2020) Kalsoom, Humaira; Rashid, Saima; Idrees, Muhammad; Safdar, Farhat; Chu, Yu-Ming; Baleanu, Dumitru; Chu, Hong-Hu
In this paper, the newly proposed concept of Raina's function and quantum calculus are utilized to anticipate the quantum behavior of two variable Ostrowski-type inequalities. This new technique is the convolution of special functions with hypergeometric and Mittag-Leffler functions, respectively. This new concept will have the option to reduce self-similitudes in the quantum attractors under investigation. We discuss the implications and other consequences of the quantum Ostrowski-type inequalities by deriving an auxiliary result for a q1q2-differentiable function by inserting Raina's functions. Meanwhile, we present a numerical scheme that can be used to derive variants for Ostrowski-type inequalities in the sense of coordinated generalized phi-convex functions with the quantum approach. This new scheme of study for varying values of parameters with the involvement of Raina's function yields extremely intriguing outcomes with an illustrative example. It is supposed that this investigation will provide new directions for the capricious nature of quantum theory.
Citation - Scopus: 3
A Novel Numerical Dynamics of Fractional Derivatives Involving Singular and Nonsingular Kernels: Designing a Stochastic Cholera Epidemic Model
(Amer inst Mathematical Sciences-aims, 2022) Jarad, Fahd; Alsubaie, Hajid; Aly, Ayman A.; Alotaibi, Ahmed; Rashid, Saima
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 - WoS: 20
Citation - Scopus: 20
Novel Aspects of Discrete Dynamical Type Inequalities Within Fractional Operators Having Generalized (h)over-Bar Mittag-Leffler Kernels and Application
(Pergamon-elsevier Science Ltd, 2021) Sultana, Sobia; Hammouch, Zakia; Jarad, Fahd; Hamed, Y. S.; Rashid, Saima
Discrete fractional calculus (DFC) has had significant advances in the last few decades, being successfully employed in the time scale domain (h) over barZ. Understanding of DFC has demonstrated a valuable improvement in neural networks and modeling in other terrains. In the context of Riemann form (ABTL), we discuss the discrete fractional operator influencing discrete Atangana-Baleanu (AB)-fractional operator having (h) over bar -discrete generalized Mittag-Leffler kernels. In the approach being presented, some new Polya-Szego and Chebyshev type inequalities introduced within discrete AB-fractional operators having h-discrete generalized Mittag-Leffler kernels. By analyzing discrete AB-fractional operators in the time scale domain Z, we can perform a comparison basis for notable outcomes derived from the aforesaid operators. This type of discretization generates novel outcomes for synchronous functions. The specification of this proposed strategy simply demonstrates its efficiency, precision, and accessibility in terms of the methodology of qualitative approach of discrete fractional difference equation solutions, including its stability, consistency, and continual reliance on the initial value for the solutions of many fractional difference equation initial value problems. The repercussions of the discrete AB-fractional operators can depict new presentations for various particular cases. Finally, applications concerning bounding mappings are also illustrated. (C) 2021 Elsevier Ltd. All rights reserved.
Citation - WoS: 7
Citation - Scopus: 7
A Peculiar Application of the Fractal-Fractional Derivative in the Dynamics of a Nonlinear Scabies Model
(Elsevier, 2022) Kanwal, Bushra; Jarad, Fahd; Elagan, S. K.; Rashid, Saima
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, R-0, 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 - WoS: 5
Citation - Scopus: 5
On New Computations of the Fractional Epidemic Childhood Disease Model Pertaining To the Generalized Fractional Derivative With Nonsingular Kernel
(Amer inst Mathematical Sciences-aims, 2022) Jarad, Fahd; Bayones, Fatimah S.; Rashid, Saima
The present research investigates the Susceptible-Infected-Recovered (SIR) epidemic model of childhood diseases and its complications with the Atangana-Baleanu fractional derivative operator in the Caputo sense (ABC). With the aid of the Elzaki Adomian decomposition method (EADM), the approximate solutions of the aforesaid model are discussed by exerting the Adomian decomposition method. By employing the fixed point postulates and the Picard-Lindelof approach, the stability, existence, and uniqueness consequences of the model are demonstrated. Furthermore, we illustrate the essential hypothesis for disease control in order to find the role of unaware infectives in the spread of childhood diseases. Besides that, simulation results and graphical illustrations are presented for various fractional-orders. A comparison analysis is shown with the previous findings. It is hoped that ABC fractional derivative and the projected algorithm will provide new venues in futuristic studies to manipulate and analyze several epidemiological models.
Citation - WoS: 15
Citation - Scopus: 26
New Quantum Estimates in the Setting of Fractional Calculus Theory
(Springer, 2020) Ashraf, Rehana; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Rashid, Saima; Hammouch, Zakia
In this article, the investigation is centered around the quantum estimates by utilizing quantum Hahn integral operator via the quantum shift operator eta psi(q)(zeta) = q zeta + (1 - q)eta, zeta is an element of [mu, nu], eta = mu+ omega/(1-q), 0 < q < 1, omega >= 0. Our strategy includes fractional calculus, Jackson's q-integral, the main ideas of quantum calculus, and a generalization used in the frame of convex functions. We presented, in general, three types of fractional quantum integral inequalities that can be utilized to explain orthogonal polynomials, and exploring some estimation problems with shifting estimations of fractional order e(1) and the q-numbers have yielded fascinating outcomes. As an application viewpoint, an illustrative example shows the effectiveness of q, omega-derivative for boundary value problem.
Citation - WoS: 9
Citation - Scopus: 9
Stochastic Dynamics of the Fractal-Fractional Ebola Epidemic Model Combining a Fear and Environmental Spreading Mechanism
(Amer inst Mathematical Sciences-aims, 2022) Jarad, Fahd; Rashid, Saima
Recent Ebola virus disease infections have been limited to human-to-human contact as well as the intricate linkages between the habitat, people and socioeconomic variables. The mechanisms of infection propagation can also occur as a consequence of variations in individual actions brought on by dread. This work studies the evolution of the Ebola virus disease by combining fear and environmental spread using a compartmental framework considering stochastic manipulation and a newly defined non-local fractal-fractional (F-F) derivative depending on the generalized Mittag-Leffler kernel. To determine the incidence of infection and person-to-person dissemination, we developed a fear-dependent interaction rate function. We begin by outlining several fundamental characteristics of the system, such as its fundamental reproducing value and equilibrium. Moreover, we examine the existence-uniqueness of non-negative solutions for the given randomized process. The ergodicity and stationary distribution of the infection are then demonstrated, along with the basic criteria for its eradication. Additionally, it has been studied how the suggested framework behaves under the F-F complexities of the Atangana-Baleanu derivative of fractional-order rho and fractal-dimension tau. The developed scheme has also undergone phenomenological research in addition to the combination of nonlinear characterization by using the fixed point concept. The projected findings are demonstrated through numerical simulations. This research is anticipated to substantially increase the scientific underpinnings for understanding the patterns of infectious illnesses across the globe.