Browsing by Author "Jarad, Fahd"

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Citation Count: Ahmed, Idris...et al. (2023). "A Caputo-Fabrizio Fractional-Order Cholera Model And İts Sensitivity Analysis", Mathematical Modelling and Numerical Simulation with Applications, Vol. 3, No. 2, pp. 170-187.
A Caputo-Fabrizio Fractional-Order Cholera Model And İts Sensitivity Analysis
(2023) Ahmed, Idris; Akgül, Ali; Jarad, Fahd; Kumam, Poom; Nonlaopon, Kamsing; 234808
In recent years, the availability of advanced computational techniques has led to a growing emphasis on fractional-order derivatives. This development has enabled researchers to explore the intricate dynamics of various biological models by employing fractional-order derivatives instead of traditional integer-order derivatives. This paper proposes a Caputo-Fabrizio fractional-order cholera epidemic model. Fixed-point theorems are utilized to investigate the existence and uniqueness of solutions. A recent and effective numerical scheme is employed to demonstrate the model’s complex behaviors and highlight the advantages of fractional-order derivatives. Additionally, a sensitivity analysis is conducted to identify the most influential parameters
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: Abbas, Sana...et al. (2023). "A Drone-Based Blood Donation Approach Using an Ant Colony Optimization Algorithm", CMES-Computer Modeling In Engineering & Sciences, Vol. 136, No. 2, pp.1917-1930.
A Drone-Based Blood Donation Approach Using an Ant Colony Optimization Algorithm
(2023) Abbas, Sana; Ashraf, Faraha; Jarad, Fahd; Sardar, Muhammad Shoaib; Siddique, Imran; 234808
This article presents an optimized approach of mathematical techniques in the medical domain by manoeuvring the phenomenon of ant colony optimization algorithm (also known as ACO). A complete graph of blood banks and a path that covers all the blood banks without repeating any link is required by applying the Travelling Salesman Problem (often TSP). The wide use promises to accelerate and offers the opportunity to cultivate health care, particularly in remote or unmerited environments by shrinking lab testing reversal times, empowering just-in-time lifesaving medical supply.
Citation Count: Ahmed, Idris...et al. "A Dynamical and Sensitivity Analysis of the Caputo Fractional-Order Ebola Virus Model: Implications for Control Measures", Science and Technology Asia, Science and Technology Asia, Vol. 28, No. 4, pp. 26-37.
A Dynamical and Sensitivity Analysis of the Caputo Fractional-Order Ebola Virus Model: Implications for Control Measures
(2023) Ahmed, Idris; Yusuf, Abdullahi; Tariboon, Jessada; Muhammad, Mubarak; Jarad, Fahd; Mikailu, Badamasi Bashir; 234808
The recurrence of outbreaks in cases of Ebola virus among African countries remains one of the greatest issues of concern. Practices such as hunting or consumption of contam-inated bush meat, unsafe funeral practices, and environmental contamination have all been implicated as possible contributors. This paper investigates the transmission dynamics of the Ebola virus model in the setting of a Caputo fractional-order derivative that accounts for both direct and indirect transmissions of the virus. By employing the concept of fixed theorems, we derived the existence and uniqueness results of the model. Moreover, we analyzed the forward normalized sensitivity indices to identify the critical parameters for controlling the infection and found that reducing the contact rate between infected individuals and susceptible vectors is vital to limiting the virus’s spread. Comparing the proposed fractional-order model with those of the previously developed integer-order model numerically, we found that the proposed model provides more reliable information on the model’s dynamics. Thus, we conclude that the Caputo fractional-order operator is a precise tool for describing the proposed model behavior and can help understand the complexities of Ebola virus disease outbreaks. © 2023, Thammasat University. All rights reserved.
Citation Count: Iqbal, Zafar...et al. (2023). "A finite difference scheme to solve a fractional order epidemic model of computer virus", Aims Mathematics, Vol.8, No. 1, pp.2337-2359.
A finite difference scheme to solve a fractional order epidemic model of computer virus
(2023) Iqbal, Zafar; Rehman, Muhammad Aziz-ur; Imran, Muhammad; Ahmed, Nauman; Fatima, Umbreen; Akgul, Ali; Rafiq, Muhammad; Raza, Ali; Djuraev, Ali Asrorovich; Jarad, Fahd
In this article, an analytical and numerical analysis of a computer virus epidemic model is presented. To more thoroughly examine the dynamics of the virus, the classical model is transformed into a fractional order model. The Caputo differential operator is applied to achieve this. The Jacobian approach is employed to investigate the model's stability. To investigate the model's numerical solution, a hybridized numerical scheme called the Grunwald Letnikov nonstandard finite difference (GL-NSFD) scheme is created. Some essential characteristics of the population model are scrutinized, including positivity boundedness and scheme stability. The aforementioned features are validated using test cases and computer simulations. The mathematical graphs are all detailed. It is also investigated how the fundamental reproduction number R0 functions in stability analysis and illness dynamics.
Citation Count: Abdeljavad, T...et al. (2010). A fite type result for sequental fractional differintial equations. Dynamic System and Applications, 19(2), 383-394.
A fite type result for sequental fractional differintial equations
(Dynamic Publisher, 2010) Abdeljawad, Thabet; Baleanu, Dumitru; Jarad, Fahd; Mustafa, Octavian G.; Trujillo, J. J.
Given the solution f of the sequential fractional differential equation aD(t)(alpha)(aD(t)(alpha) f) + P(t)f = 0, t is an element of [b, a], where -infinity < a < b < c < + infinity, alpha is an element of (1/2, 1) and P : [a, + infinity) -> [0, P(infinity)], P(infinity) < + infinity, is continuous. Assume that there exist t(1),t(2) is an element of [b, c] such that f(t(1)) = (aD(t)(alpha))(t(2)) = 0. Then, we establish here a positive lower bound for c - a which depends solely on alpha, P(infinity). Such a result might be useful in discussing disconjugate fractional differential equations and fractional interpolation, similarly to the case of (integer order) ordinary differential equations
Citation Count: Rehman, Aziz Ur; Jarad, Fahd; Riaz, Muhammad Bilal (2024). "A FRACTIONAL STUDY OF MHD CASSON FLUID MOTION WITH THERMAL RADIATIVE FLUX AND HEAT INJECTION/SUCTION MECHANISM UNDER RAMPED WALL CONDITION: APPLICATION OF RABOTNOV EXPONENTIAL KERNEL", Acta Mechanica et Automatica, Vol. 18, No. 1, pp. 84-92.
A FRACTIONAL STUDY OF MHD CASSON FLUID MOTION WITH THERMAL RADIATIVE FLUX AND HEAT INJECTION/SUCTION MECHANISM UNDER RAMPED WALL CONDITION: APPLICATION OF RABOTNOV EXPONENTIAL KERNEL
(2024) Rehman, Aziz Ur; Jarad, Fahd; Riaz, Muhammad Bilal; 234808
The primary objective of this research is to extend the concept of fractionalized Casson fluid flow. In this study, a comprehensive analysis of magnetohydrodynamic (MHD) natural convective flow of Casson fluid is conducted, focusing on obtaining analytical solutions using the non-integer-order derivative known as the Yang–Abdel-Aty–Cattani (YAC) operator. The YAC operator utilized in this research possesses a more generalized exponential kernel. The fluid flow is examined in the vicinity of an infinitely vertical plate with a characteristic velocity denoted as u80. The mathematical modelling of the problem incorporates partial differential equations, incorporating Newtonian heating and ramped conditions. To facilitate the analysis, a suitable set of variables is introduced to transform the governing equations into a dimensionless form. The Laplace transform (LT) is then applied to the fractional system of equations, and the obtained results are presented in series form and also expressed in terms of special functions. The study further investigates the influence of relevant parameters, such as α, β, Pr, Q, Gr, M, Nr and K, on the fluid flow to reveal interesting findings. A comparison of different approaches reveals that the YAC method yields superior results compared to existing operators found in the literature. Graphs are generated to illustrate the outcomes effectively. Additionally, the research explores the limiting cases of the Casson and viscous fluid models to derive the classical form from the YAC fractionalized Casson fluid model. © 2024 Sciendo. All rights reserved.
Citation Count: Abdeljawad, T., Alzabut, J., Jarad, F. (2017). A generalized Lyapunov-type inequality in the frame of conformable derivatives. Advance in Difference Equations, 321. http://dx.doi.org/10.1186/s13662-017-1383-z
A generalized Lyapunov-type inequality in the frame of conformable derivatives
(Springer, 2017) Abdeljawad, Thabet; Alzabut, Jehad; Jarad, Fahd; 234808
We prove a generalized Lyapunov-type inequality for a conformable boundary value problem (BVP) of order alpha is an element of (1, 2]. Indeed, it is shown that if the boundary value problem (T(alpha)(c)x)(t) + r(t) x(t) = 0, t is an element of (c, d), x(c) = x(d) = 0 has a nontrivial solution, where r is a real-valued continuous function on [c, d], then integral(d)(c) vertical bar r(t)vertical bar dt > alpha(alpha)/(alpha - 1)(alpha-1) (d - c)(a-1). (1) Moreover, a Lyapunov type inequality of the form integral(d)(c)vertical bar r(t)vertical bar dt > 3 alpha - 1/(d - c)(2 alpha-1) (3 alpha - 1/2 alpha - 1)(2 alpha-1/a), 1/2 < alpha <= 1, (2) is obtained for a sequential conformable BVP. Some examples are given and an application to conformable Sturm-Liouville eigenvalue problem is analyzed.
Citation Count: Talib, Imran...et al. (2022). "A generalized operational matrix of mixed partial derivative terms with applications to multi-order fractional partial differential equations", Alexandria Engineering Journal, Vol. 61, No. 1, pp. 135-145.
A generalized operational matrix of mixed partial derivative terms with applications to multi-order fractional partial differential equations
(2022) Talib, Imran; Jarad, Fahd; Mirza, Muhammad Umar; Nawaz, Asma; Riaz, Muhammad Bilal; 234808
In this paper, a computational approach based on the operational matrices in conjunction with orthogonal shifted Legendre polynomials (OSLPs) is designed to solve numerically the multi-order partial differential equations of fractional order consisting of mixed partial derivative terms. Our computational approach has ability to reduce the fractional problems into a system of Sylvester types matrix equations which can be solved by using MATLAB builtin function lyap (.). The solution is approximated as a basis vectors of OSLPs. The efficiency and the numerical stability is examined by taking various test examples. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.
Citation Count: Alzabut, Jehad...et al. (2019). "A Gronwall inequality via the generalized proportional fractional derivative with applications", Journal of Inequalities and Applications.
A Gronwall inequality via the generalized proportional fractional derivative with applications
(Springer Open, 2019) Alzabut, Jehad; Abdeljawad, Thabet; Jarad, Fahd; Sudsutad, Weerawat; 234808
In this paper, we provide a new version for the Gronwall inequality in the frame of the generalized proportional fractional derivative. Prior to the main results, we introduce the generalized proportional fractional derivative and expose some of its features. As an application, we accommodate the newly defined derivative to prove the uniqueness and obtain a bound in terms of Mittag-Leffler function for the solutions of a nonlinear delay proportional fractional system. An example is presented to demonstrate the applicability of the theory.
Citation Count: Ahmad, Shabir;...et.al. (2022). "A hybrid analytical technique for solving nonlinear fractional order PDEs of power law kernel: Application to KdV and Fornberg-Witham equations", AIMS Mathematics, Vol.7, No.5, pp.9389-9404.
A hybrid analytical technique for solving nonlinear fractional order PDEs of power law kernel: Application to KdV and Fornberg-Witham equations
(2022) Ahmad, Shabir; Ullah, Aman; Akgül, Ali; Jarad, Fahd; 234808
It is important to deal with the exact solution of nonlinear PDEs of non-integer orders. Integral transforms play a vital role in solving differential equations of integer and fractional orders. To obtain analytical solutions to integer and fractional-order DEs, a few transforms, such as Laplace transforms, Sumudu transforms, and Elzaki transforms, have been widely used by researchers. We propose the Yang transform homotopy perturbation (YTHP) technique in this paper. We present the relation of Yang transform (YT) with the Laplace transform. We find a formula for the YT of fractional derivative in Caputo sense. We deduce a procedure for computing the solution of fractional-order nonlinear PDEs involving the power-law kernel. We show the convergence and error estimate of the suggested method. We give some examples to illustrate the novel method. We provide a comparison between the approximate solution and exact solution through tables and graphs.
Citation Count: Rana, Gule;...et.al. "A Modified Algorithm Based on Haar Wavelets for the Numerical Simulation of Interface Models", Journal of Function Spaces, Vol.2022.
A Modified Algorithm Based on Haar Wavelets for the Numerical Simulation of Interface Models
(2022) Rana, Gule; Asif, Muhammad; Haider, Nadeem; Bilal, Rubi; Ahsan, Muhammad; Al-Mdallal, Qasem; Jarad, Fahd; 234808
In this paper, a new numerical technique is proposed for the simulations of advection-diffusion-reaction type elliptic and parabolic interface models. The proposed technique comprises of the Haar wavelet collocation method and the finite difference method. In this technique, the spatial derivative is approximated by truncated Haar wavelet series, while for temporal derivative, the finite difference formula is used. The diffusion coefficients, advection coefficients, and reaction coefficients are considered discontinuously across the fixed interface. The newly established numerical technique is applied to both linear and nonlinear benchmark interface models. In the case of linear interface models, Gauss elimination method is used, whereas for nonlinear interface models, the nonlinearity is removed by using the quasi-Newton linearization technique. The L∞ errors are calculated for different number of collocation points. The obtained numerical results are compared with the immersed interface method. The stability and convergence of the method are also discussed. On the whole, the numerical results show more efficiency, better accuracy, and simpler applicability of the newly developed numerical technique compared to the existing methods in literature.
Citation Count: Jarad, Fahd; Thabet, Abdeljawad, "A modified Laplace transform for certain generalized fractional operators", Results in Nonlinear Analysis, No.2, pp.88-98, (2018).
A modified Laplace transform for certain generalized fractional operators
(2018) Jarad, Fahd; Thabet, Abdeljawad; 234808
It is known that Laplace transform converges for functions of exponential order. In order to extend the possibility of working in a large class of functions, we present a modified Laplace transform that we call ρ-Laplace transform, study its properties and prove its own convolution theorem. Then, we apply it to solve some ordinary differential equations in the frame of a certain type generalized fractional derivatives. This modified transform acts as a powerful tool in handling the kernels of these generalized fractional operators
Citation Count: Foroutan, Mohammad Reza;...et.al. (2022). "A new application of the Legendre reproducing kernel method", AIMS Mathematics, Vol.7, No.6, pp.10671-10670.
A new application of the Legendre reproducing kernel method
(2022) Foroutan, Mohammad Reza; Hashemi, Mir Sajjad; Gholizadeh, Leila; Akgül, Ali; Jarad, Fahd; 234808
n this work, we apply the reproducing kernel method to coupled system of second and fourth order boundary value problems. We construct a novel algorithm to acquire the numerical results of the nonlinear boundary-value problems. We also use the Legendre polynomials. Additionally, we discuss the convergence analysis and error estimates. We demonstrate the numerical simulations to prove the efficiency of the presented method.
Citation Count: Saleem, Naeem...et al. (2023). "A New Iteration Scheme for Approximating Common Fixed Points in Uniformly Convex Banach Spaces", Journal of Mathematics, Vol. 2023.
A New Iteration Scheme for Approximating Common Fixed Points in Uniformly Convex Banach Spaces
(2023) Saleem, Naeem; Agwu, Imo Kalu; Ishtiaq, Umar; Jarad, Fahd; 234808
In this paper, frstly, we introduce a method for fnding common fxed point of L-Lipschitzian and total asymptotically strictly pseudo-non-spreading self-mappings and L-Lipschitzian and total asymptotically strictly pseudo-non-spreading non-self-mappings in the setting of a real uniformly convex Banach space. Secondly, the demiclosedness principle for total asymptotically strictly pseudo-non-spreading non-self-mappings is established. Tirdly, the weak convergence theorems of the proposed method to the common fxed point of the above mappings are proved. Our results improved, extended, and generalized some corresponding results in the literature. Copyright © 2023 Naeem Saleem et al.
A NEW NUMERICAL TREATMENT FOR FRACTIONAL DIFFERENTIAL EQUATIONS BASED ON NON-DISCRETIZATION OF DATA USING LAGUERRE POLYNOMIALS
(2020) Khan, Adnan; Shah, Kamal; Arfan, Muhammad; Abdeljawad, Thabet; Jarad, Fahd; 234808
In this research work, we discuss an approximation techniques for boundary value problems (BVPs) of differential equations having fractional order (FODE). We avoid the method from discretization of data by applying polynomials of Laguerre and developed some matrices of operational types for the obtained numerical solution. By applying the operational matrices, the given problem is converted to some algebraic equation which on evaluation gives the required numerical results. These equations are of Sylvester types and can be solved by using matlab. We present some testing examples to ensure the correctness of the considered techniques.
Citation Count: Jarad, F., Kaymakçalan, B., Taş, K. (2012). A new transform method in nabla discrete fractional calculus. Advance in Difference Equations. http://dx.doi.org/10.1186/1687-1847-2012-190
A new transform method in nabla discrete fractional calculus
(Springer International Publishing, 2012) Jarad, Fahd; Kaymakçalan, Billur; Taş, Kenan; 4971
Starting from the definition of the Sumudu transform on a general nabla time scale, we define the generalized nabla discrete Sumudu transform. We obtain the nabla discrete Sumudu transform of Taylor monomials, fractional sums, and differences. We apply this transform to solve some fractional difference equations with initial value problems.
Citation Count: Asjad, Muhammad Imran;...et.al. (2022). "A Nonsingular Fractional Derivative Approach for Heat and Mass Transfer Flow with Hybrid Nanoparticles", Journal of Mathematics, Vol.2022.
A Nonsingular Fractional Derivative Approach for Heat and Mass Transfer Flow with Hybrid Nanoparticles
(2022) Asjad, Muhammad Imran; Naz, Rabia; Ikram, Muhammad Danish; Iqbal, Azhar; Jarad, Fahd; 234808
This paper deals with the study of MHD Brinkman type fluid flow containing hybrid titanium (TiO2) and silver (Ag) nanoparticles with nonlocal noninteger type Atangana-Baleanu (ABC) fractional differential operator. The problem is designed for the convective flow restrained in a microchannel. With the Mittag-Leffler kernel, the conventional governing equations are converted into dimensionless form and then generalised with noninteger order fractional operators. The solutions for temperature and velocity fields obtained via Laplace transform method and expressed in the series form. The effect of related parameters is dignified graphically with the help of Mathcad and presented in the graphical section. Finally, the results show that the AB fractional operator exhibited improved memory effect as compared to CF fractional operator. Furthermore, due to increasing the values volume fractional temperature can be enhanced and velocity decreases. In comparison between nanoparticles for different types of based fluid, velocity and temperature of water based (TiO2) and silver (Ag) is higher than other base fluids.
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.