Browsing by Author "Jarad, F."

Now showing 1 - 20 of 21

Citation - Scopus: 23
A Caputo-Fabrizio Fractional-Order Cholera Model And İts Sensitivity Analysis
(Mehmet Yavuz, 2023) Ahmed, I.; Jarad, Fahd; Akgül, A.; Jarad, F.; Kumam, P.; Nonlaopon, K.; 234808; Matematik
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. © 2023 by the authors.
Citation - Scopus: 7
A Dynamical and Sensitivity Analysis of the Caputo Fractional-Order Ebola Virus Model: Implications for Control Measures
(Thammasat University, 2023) Ahmed, I.; Jarad, Fahd; Yusuf, A.; Tariboon, J.; Muhammad, M.; Jarad, F.; Mikailu, B.B.; 234808; Matematik
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 - WoS: 8
Citation - Scopus: 8
A novel fractional piecewise linear map: regular and chaotic dynamics
(Taylor & Francis Ltd, 2021) Bououden, R.; Jarad, Fahd; Abdelouahab, M. S.; Jarad, F.; Hammouch, Z.; 234808; Matematik
In this paper, a new piecewise linear map of the plan and its fractional version deduced from the Lozi map is introduced and analysed. The main attention is paid to the study of fixed points and their stability, cycles of period two and their stability regions and the type of bifurcation that occur in the dynamical behaviours of this map. The routes to chaos and some chaotic attractors that exist in the behaviour of the integer map are discussed. Finally, the chaotic behaviour of the associated proposed fractional map is analysed by means of bifurcations diagrams.
Citation - WoS: 7
Citation - Scopus: 7
A numerical method for distributed-order time fractional 2D Sobolev equation
(Elsevier, 2023) Heydari, M. H.; Rashid, S.; Jarad, F.; 234808
In this work, the distributed-order time fractional 2D Sobolev equation is introduced. The orthonormal Bernoulli polynomials, as a renowned family of basis functions, are employed to solve this problem. To effectively use of these polynomials in constructing a suitable methodology for this equation, some operational matrices regarding the ordinary and fractional derivative of them are derived. In the developed method, by approximating the unknown solution by means of these polynomials and using the mentioned matrices, as well as applying the collocation technique, a system of algebraic equations (in which the unknowns are the expansion coefficients of the solution function) is obtained, which by solving it, a solution for the main problem is obtained. By providing four test problems, the capability and accuracy of the scheme are studied.
Citation - Scopus: 0
A special issue in honor of the 55th birthday of dumitru baleanu
(Cankaya University, 2019) Jarad, F.; Jarad, Fahd; 234808; Matematik
Citation - Scopus: 3
A special issue:Recent developments in nonlinear partial differential equations
(Erdal Karapinar, 2020) Abdeljawad, T.; Al-Mdallal, Q.M.; Hammouch, Z.; Jarad, F.; F.
Citation - Scopus: 5
Chaos in new 2-d discrete mapping and its application in optimization
(InforMath Publishing Group, 2020) Bououden, R.; Jarad, Fahd; Abdelouahab, M.S.; Jarad, F.; 234808; Matematik
In this paper, we propose a new map which is a combination of the Hénon and Lozi maps. We analyze the proposed map numerically and with the aid of bifurcation plots. On the other hand, and as an example of application of this new map, we are going to use it in the chaotic optimisation algorithm. To prove the efficiency of this map, we use numerical results thorought the paper. © 2020 InforMath Publishing Group
Citation - Scopus: 48
Development of TOPSIS Technique under Pythagorean Fuzzy Hypersoft Environment Based on Correlation Coefficient and Its Application towards the Selection of Antivirus Mask in COVID-19 Pandemic
(Hindawi Limited, 2021) Zulqarnain, R.M.; Jarad, Fahd; Siddique, I.; Jarad, F.; Ali, R.; Abdeljawad, T.; 234808; Matematik
The correlation coefficient between two variables plays an important role in statistics. Also, the accuracy of relevance assessment depends on information from a set of discourses. The data collected from numerous statistical studies are full of exceptions. The Pythagorean fuzzy hypersoft set (PFHSS) is a parameterized family that deals with the subattributes of the parameters and an appropriate extension of the Pythagorean fuzzy soft set. It is also the generalization of the intuitionistic fuzzy hypersoft set (IFHSS), which is used to accurately assess insufficiency, anxiety, and uncertainties in decision-making. The PFHSS can accommodate more uncertainties compared to the IFHSS, and it is the most substantial methodology to describe fuzzy information in the decision-making process. The core objective of the this study is to develop the notion and features of the correlation coefficient and the weighted correlation coefficient for PFHSS and to introduce the aggregation operators such as Pythagorean fuzzy hypersoft weighted average (PFHSWA) and Pythagorean fuzzy hypersoft weighted geometric (PFHSWG) operators under the PFHSS scenario. A prioritization technique for order preference by similarity to the ideal solution (TOPSIS) under PFHSS based on correlation coefficients and weighted correlation coefficients is presented. Through the developed methodology, a technique for solving multiattribute group decision-making (MAGDM) problem is planned. Also, the importance of the developed methodology and its application in indicating multipurpose antivirus mask throughout the COVID-19 pandemic period is presented. A brief comparative analysis is described with the advantages, effectiveness, and flexibility of numerous existing studies that demonstrate the effectiveness of the proposed method. © 2021 Rana Muhammad Zulqarnain et al.
Citation - Scopus: 0
Existence of Solutions of Multi-Order Fractional Differential Equations
(Elsevier B.V., 2025) Bouchelaghem, F.; Boulares, H.; Ardjouni, A.; Jarad, F.; Abdeljawad, T.; Abdalla, B.; Shah, K.
Recently, the field of fractional calculus has garnered significant attention due to its wide range of applications across various disciplines in science and engineering. Numerous results have been derived using tools from numerical functional analysis and fixed point theory to address a variety of problems in this area. This study employs the Banach Fixed Point Theorem (BFPT) to establish the existence and uniqueness of solutions for Riemann–Liouville fractional differential equations (RLFDEs) involving multiple orders. Sufficient conditions for the existence of solutions to the problem under consideration have been provided. Furthermore, an illustrative example is presented to validate the theoretical findings. © 2025
Citation - Scopus: 18
Mittag-Leffler form solutions of natural convection flow of second grade fluid with exponentially variable temperature and mass diffusion using Prabhakar fractional derivative
(Elsevier Ltd, 2022) Rehman, A.U.; Jarad, Fahd; Awrejcewicz, J.; Riaz, M.B.; Jarad, F.; 234808; Matematik
In this article, heat source impact on unsteady magnetohydrodynamic (MHD) flows of Prabhakar-like non integer second grade fluid near an exponentially accelerated vertical plate with exponentially variable velocity, temperature and mass diffusion through a porous medium. For the sake of generalized memory effects, a new mathematical fractional model is formulated based on newly introduced Prabhakar fractional operator with generalized Fourier's law and Fick's law. This fractional model has been solved analytically and exact solutions for dimensionless velocity, concentration and energy equations are calculated in terms of Mittag-Leffler functions by employing the Laplace transformation method. Physical impacts of different parameters such as α, Pr, β, Sc, Gr, γ, Gm are studied and demonstrated graphically by Mathcad software. Furthermore, to validate our current results, some limiting models such as classical second grade model, classical Newtonian model and fractional Newtonian model are recovered from Prabhakar fractional second grade fluid. Moreover, compare the results between second grade and Newtonian fluids for both fractional and classical which shows that the movement of the viscous fluid is faster than second grade fluid. Additionally, it is visualized that for both classical second grade and viscous fluid have relatively higher velocity as compared to fractional second grade and viscous fluid. © 2022 The Authors.
Citation - Scopus: 13
Multicriteria Decision-Making Approach for Pythagorean Fuzzy Hypersoft Sets' Interaction Aggregation Operators
(Hindawi Limited, 2021) Zulqarnain, R.M.; Siddique, I.; Ali, R.; Jarad, F.; Iampan, A.
In this paper, we examine the multicriteria decision-making (MCDM) difficulties for Pythagorean fuzzy hypersoft sets (PFHSSs). The PFHSSs are a suitable extension of the Pythagorean fuzzy soft sets (PFSSs) which deliberates the parametrization of multi-subattributes of considered parameters. It is a most substantial notion for describing fuzzy information in the decision-making (DM) procedure to accommodate more vagueness comparative to existing PFSSs and intuitionistic fuzzy hypersoft sets (IFHSSs). The core objective of this study is to plan some innovative operational laws considering the interaction for Pythagorean fuzzy hypersoft numbers (PFHSNs). Also, based on settled interaction operational laws, two aggregation operators (AOs) i.e., Pythagorean fuzzy hypersoft interaction weighted average (PFHSIWA) and Pythagorean fuzzy hypersoft interaction weighted geometric (PFHSIWG) operators for PFHSSs operators have been presented with their fundamental properties. Furthermore, an MCDM technique has been established using planned interaction AOs. To ensure the strength and practicality of the developed MCDM method, a mathematical illustration has been presented. The usefulness, influence, and versatility of the developed method have been demonstrated via comparative analysis with the help of some conventional studies. © 2021 Rana Muhammad Zulqarnain et al.
Citation - Scopus: 3
Numerical Construction of Lyapunov Functions Using Homotopy Continuation Method
(DergiPark, 2022) Ibrahim, A.; Jarad, Fahd; Bala, S.I.; Ahmed, I.; Ibrahim, M.J.; Jarad, F.; 234808; Matematik
Lyapunov functions are commonly involved in the analysis of the stability of linear and nonlinear dynamical systems. Despite the fact that there is no generic procedure for creating these functions, many authors use polynomials in p-forms as candidates for constructing Lyapunov functions, while others restrict the construction to quadratic forms. We proposed a method for constructing polynomial Lyapunov functions that are not necessary in a form by focusing on the positive and negative definiteness of the Lyapunov candidate and the Hessian of its derivative, as well as employing the sum of square decomposition. The idea of Newton polytopes was used to transform the problem into a system of algebraic equations that were solved using the polynomial homotopy continuation method. Our method can produce several possibilities of Lyapunov functions for a given candidate. The sample test conducted demonstrates that the method developed is promising. © 2022, DergiPark. All rights reserved.
Citation - Scopus: 4
Numerical Evaluation for the Peristaltic Flow in the Proximity of Double-Diffusive Convection of Non-Newtonian Nanofluid Under the Mhd
(Elsevier B.V., 2024) Riaz, M.B.; Hussain, A.; Saddiqa, A.; Jarad, F.
This article mainly studies the 2-D propagation of a non-compressible Eyring-Powell nanofluid flow through a stretched wedge under the Magneto-hydrodynamic effect. Equations for temperature, concentration, double-diffusive convection and momentum are taken into consideration. Since solving the dimensionless equations associated with our study is an uphill task, we utilize the MATLAB bvp4c solver to illustrate the graphical performance of different parameters. This manuscript may be significant in the projects in the field of industry and medicine. The manuscript's noteworthy features include the magnetic field, heat source-sink parameter, double diffusivity, and solar radiation process. The main finding is that the local fluid parameter k1 and magnetic field parameter M decelerate the velocity of nanofluid. Because different nanoparticles have different effects on fluids, the fluid's temperature exhibits multiple behaviors, therefore by escalating the Prandtl number initially, it increases and then decelerates due to the presence of nanoparticles. The concentration of fluid declines as the Schmidt number rises. The double diffusivity of Eyring-Powell nanofluid improves with magnification in the fluid's Schmidt number Sc and Prandtl number Pr. © 2024 The Author(s)
Citation - Scopus: 2
On abstract Cauchy problems in the frame of a generalized Caputo type derivative
(DergiPark, 2023) Jarad, Fahd; Bourchi, S.; Jarad, F.; Abdeljawad, Thabet; Adjabi, Y.; Abdeljawad, T.; Mahariq, I.; 234808; Matematik
In this paper, we consider a class of abstract Cauchy problems in the framework of a generalized Caputo type fractional. We discuss the existence and uniqueness of mild solutions to such a class of fractional differential equations by using properties found in the related fractional calculus, the theory of uniformly continuous semigroups of operators and the fixed point theorem. Moreover, we discuss the continuous dependence on parameters and Ulam stability of the mild solutions. At the end of this paper, we bring forth some examples to endorse the obtained results. © 2023, DergiPark. All rights reserved.
Citation - WoS: 15
Citation - Scopus: 15
On fractional differential inclusion problems involving fractional order derivative with respect to another function
(World Scientific Publ Co Pte Ltd, 2020) Jarad, Fahd; Belmor, Samiha; Jarad, F.; Abdeljawad, Thabet; Abdeljawad, T.; Alqudah, Manar A.; 234808; Matematik
In this research work, we investigate the existence of solutions for a class of nonlinear boundary value problems for fractional-order differential inclusion with respect to another function. Endpoint theorem for phi-weak contractive maps is the main tool in determining our results. An example is presented in aim to illustrate the results.
Citation - Scopus: 3
On Mittag-Leffler Kernel-Dependent Fractional Operators with Variable Order
(Springer International Publishing, 2019) Abdeljawad, Thabet; Bahaa, G.M.; Abdeljawad, T.; Jarad, Fahd; Jarad, F.; 234808; Matematik
In this work, integration by parts formulas for variable-order fractional operators with Mittag-Leffler kernels are presented and applied to study constrained fractional variational principles involving variable-order Caputo-type Atangana–Baleanu’s derivatives, where the variable-order fractional Euler–Lagrange equations are investigated. A general formulation of fractional Optimal Control Problems (FOCPs) and a solution scheme for such class of systems are proposed. The performance index of a FOCP is taken into consideration as function of state as well as control variables. © 2019, Springer Nature Singapore Pte Ltd.
Citation - Scopus: 6
On the discrete laplace transform
(Cankaya University, 2019) Ameen, R.; Jarad, Fahd; Köse, H.; Jarad, F.; 234808; Matematik
The objective of this paper is to introduce the discrete Laplace transform. Basic theorems related to this transformation are mentioned and the discrete Laplace transform of basic functions are given. © 2019, Cankaya University. All rights reserved.
Citation - WoS: 81
Citation - Scopus: 82
On the weighted fractional operators of a function with respect to another function
(World Scientific Publ Co Pte Ltd, 2020) Jarad, Fahd; Jarad, F.; Abdeljawad, T.; Abdeljawad, Thabet; Shah, K.; 234808; Matematik
The primary goal of this study is to define the weighted fractional operators on some spaces. We first prove that the weighted integrals are bounded in certain spaces. Afterwards, we discuss the weighted fractional derivatives defined on absolute continuous-like spaces. At the end, we present a modified Laplace transform that can be applied perfectly to such operators.
Citation - Scopus: 6
Particle Swarm Optimization for Solving Sine-Gordan Equation
(Tech Science Press, 2023) Arora, G.; Jarad, Fahd; Chauhan, P.; Asjad, M.I.; Joshi, V.; Emadifar, H.; Jarad, F.; 234808; Matematik
The term 'optimization' refers to the process of maximizing the beneficial attributes of a mathematical function or system while minimizing the unfavorable ones. The majority of real-world situations can be modelled as an optimization problem. The complex nature of models restricts traditional optimization techniques to obtain a global optimal solution and paves the path for global optimization methods. Particle Swarm Optimization is a potential global optimization technique that has been widely used to address problems in a variety of fields. The idea of this research is to use exponential basis functions and the particle swarm optimization technique to find a numerical solution for the Sine-Gordan equation, whose numerical solutions show the soliton form and has diverse applications. The implemented optimization technique is employed to determine the involved parameter in the basis functions, which was previously approximated as a random number in the work reported till now in the literature. The obtained results are comparable with the results obtained in the literature. The work is presented in the form of figures and tables and is found encouraging. © 2023 Authors. All rights reserved.
Citation - Scopus: 1
Some properties for certain subclasses of analytic functions associated with k−integral operators
(Erdal Karapinar, 2020) Abdeljawad, Thabet; Abujarad, E.S.A.; Abujarad, M.H.A.; Jarad, Fahd; Abdeljawad, T.; Jarad, F.; 234808; Matematik
In this paper, the k-integral operators for analytic functions defined in the open unit disc U = {z ∈ C: |z| < 1} are introduced. Several new subclasses of analytic functions satisfying certain relations involving these operators are also introduced. Further, we establish the inclusion relation for these subclasses. Next, the integral preserving properties of a k-integral operator satisfied by these newly introduced subclasses are obtained. Some applications of the results are discussed. Concluding remarks are also given. © 2020, Erdal Karapinar. All rights reserved.