Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 6Citation - Scopus: 6Modeling the Transmission Dynamics of Middle Eastern Respiratory Syndrome Coronavirus with the Impact of Media Coverage(Elsevier, 2021) Fatima, BiBi; Alqudah, Manar A.; Zaman, Gul; Jarad, Fahd; Abdeljawad, ThabetMiddle East respiratory syndrome coronavirus has been persistent in the Middle East region since 2012. In this paper, we propose a deterministic mathematical model to investigate the effect of media coverage on the transmission and control of Middle Eastern respiratory syndrome coronavirus disease. In order to do this we develop model formulation. Basic reproduction number R-0 will be calculated from the model to assess the transmissibility of the (MERS-CoV). We discuss the existence of backward bifurcation for some range of parameters. We also show stability of the model to figure out the stability condition and impact of media coverage. We show a special case of the model for which the endemic equilibrium is globally asymptotically stable. Finally all the theoretical results will be verified with the help of numerical simulation for easy understanding.Article Citation - WoS: 14Citation - Scopus: 14Boundary Value Problem of Weighted Fractional Derivative of a Function With a Respect To Another Function of Variable Order(Springer, 2023) Jarad, Fahd; Alqudah, Manar A.; Abdeljawad, Thabet; Benia, Kheireddine; Souid, Mohammed SaidThis study aims to resolve weighted fractional operators of variable order in specific spaces. We establish an investigation on a boundary value problem of weighted fractional derivative of one function with respect to another variable order function. It is essential to keep in mind that the symmetry of a transformation for differential equations is connected to local solvability, which is synonymous with the existence of solutions. As a consequence, existence requirements for weighted fractional derivative of a function with respect to another function of constant order are necessary. Moreover, the stability with in Ulam-Hyers-Rassias sense is reviewed. The outcomes are derived using the Kuratowski measure of non-compactness. A model illustrates the trustworthiness of the observed results.Article Citation - WoS: 8Citation - Scopus: 8Qualitative Analysis of a Fuzzy Volterra-Fredholm Integrodifferential Equation With an Atangana-Baleanu Fractional Derivative(Amer inst Mathematical Sciences-aims, 2022) Shah, Kamal; Jarad, Fahd; Abdo, Mohammed S.; Abdeljawad, Thabet; Almalahi, Mohammed A.; Panchal, Satish K.The point of this work was to analyze and investigate the sufficient conditions of the existence and uniqueness of solutions for the nonlinear fuzzy fractional Volterra Fredholm integrodifferential equation in the frame of the Atangana-Baleanu-Caputo fractional derivative methodology. To begin with, we give the parametric interval form of the Atangana-Baleanu-Caputo fractional derivative on fuzzy set-valued functions. Then, by employing Schauder???s and Banach???s fixed point procedures, we examine the existence and uniqueness of solutions for fuzzy fractional Volterra Fredholm integro-differential equation with the Atangana-Baleanu-Caputo fractional operator. It turns out that the last interval model is a combined arrangement of nonlinear equations. In addition, we consider results by applying the Adams Bashforth fractional technique and present two examples that have been numerically solved using graphs.Article Citation - WoS: 27Citation - Scopus: 28On Dynamic Systems in the Frame of Singular Function Dependent Kernel Fractional Derivatives(Mdpi, 2019) Jarad, Fahd; Sene, Ndolane; Abdeljawad, Thabet; Madjidi, FadilaIn this article, we discuss the existence and uniqueness theorem for differential equations in the frame of Caputo fractional derivatives with a singular function dependent kernel. We discuss the Mittag-Leffler bounds of these solutions. Using successive approximation, we find a formula for the solution of a special case. Then, using a modified Laplace transform and the Lyapunov direct method, we prove the Mittag-Leffler stability of the considered system.Article Citation - WoS: 1Citation - Scopus: 2N-Dimensional Fractional Frequency Laplace Transform by the Inverse Difference Operator(Hindawi Ltd, 2020) Xavier, G. Britto Antony; Jarad, Fahd; Meganathan, M.; Abdeljawad, ThabetWith the study of extensive literature on the Laplace transform with one and two variables and its properties, applications are available, but there is no work onn-dimensional Laplace transform. In this research article, we definen-dimensional fractional frequency Laplace transform with shift values. Several theorems are derived with properties of the Laplace transform. The results are numerically analyzed and discussed through MATLAB.Article Citation - WoS: 10Citation - Scopus: 13Existence and Uniqueness Results for Φ-Caputo Implicit Fractional Pantograph Differential Equation With Generalized Anti-Periodic Boundary Condition(Springer, 2020) Abdeljawad, Thabet; Jarad, Fahd; Borisut, Piyachat; Demba, Musa Ahmed; Kumam, Wiyada; Ahmed, Idris; Kumam, PoomThe present paper describes the implicit fractional pantograph differential equation in the context of generalized fractional derivative and anti-periodic conditions. We formulated the Green's function of the proposed problems. With the aid of a Green's function, we obtain an analogous integral equation of the proposed problems and demonstrate the existence and uniqueness of solutions using the techniques of the Schaefer and Banach fixed point theorems. Besides, some special cases that show the proposed problems extend the current ones in the literature are presented. Finally, two examples were given as an application to illustrate the results obtained.Article A pair of Köthe spaces between which all continuous linear operators are bounded(2004) Abdeljawad, ThabetArticle Citation - WoS: 4Citation - Scopus: 4Positivity Analysis for Mixed Order Sequential Fractional Difference Operators(Amer inst Mathematical Sciences-aims, 2022) Abdeljawad, Thabet; Sahoo, Soubhagya Kumar; Abualnaja, Khadijah M.; Mohammed, Pshtiwan Othman; Baleanu, DumitruWe consider the positivity of the discrete sequential fractional operators ((RL)(a0+1) del(v1) (RL)(a0) del(v2) f) (tau) defined on the set D-1 (see (1.1) and Figure 1) and (RL)(a0+2) del(v1) (RL)(a0) del(v2) f) (tau) of mixed order defined on the set D-2 (see (1.2) and Figure 2) for tau is an element of N-a0. By analysing the first sequential operator, we reach that (del f(tau) >= 0; for each tau is an element of Na0+1. Besides, we obtain (del f(tau) >= 0 by analysing the second sequential operator. Furthermore, some conditions to obtain the proposed monotonicity results are summarized. Finally, two practical applications are provided to illustrate the efficiency of the main theorems.Article Citation - WoS: 37Citation - Scopus: 42On Nonlinear Conformable Fractional Order Dynamical System Via Differential Transform Method(Tech Science Press, 2023) Jarad, Fahd; Al-Mdallal, Qasem; Shah, Kamal; Abdeljawad, ThabetThis article studies a nonlinear fractional order Lotka-Volterra prey-predator type dynamical system. For the proposed study, we consider the model under the conformable fractional order derivative (CFOD). We investigate the mentioned dynamical system for the existence and uniqueness of at least one solution. Indeed, Schauder and Banach fixed point theorems are utilized to prove our claim. Further, an algorithm for the approximate analytical solution to the proposed problem has been established. In this regard, the conformable fractional differential transform (CFDT) technique is used to compute the required results in the form of a series. Using Matlab-16, we simulate the series solution to illustrate our results graphically. Finally, a comparison of our solution to that obtained for the Caputo fractional order derivative via the perturbation method is given.Article Citation - WoS: 8Citation - Scopus: 8On Convexity Analysis for Discrete Delta Riemann-Liouville Fractional Differences Analytically and Numerically(Springer, 2023) Srivastava, Hari Mohan; Al-Sarairah, Eman; Abdeljawad, Thabet; Hamed, Y. S.; Baleanu, Dumitru; Mohammed, Pshtiwan OthmanIn this paper, we focus on the analytical and numerical convexity analysis of discrete delta Riemann-Liouville fractional differences. In the analytical part of this paper, we give a new formula for the discrete delta Riemann-Liouville fractional difference as an alternative definition. We establish a formula for the delta(2), which will be useful to obtain the convexity results. We examine the correlation between the positivity of ((RL)(w0)delta(alpha)f)(t) and convexity of the function. In view of the basic lemmas, we define two decreasing subsets of (2, 3), H(k,E )and M-k,M-E. The decrease of these sets allows us to obtain the relationship between the negative lower bound of ((RL)(w0)delta(alpha)f)(t) and convexity of the function on a finite time set N-w0(P) := {w(0), w(0) + 1, w(0) + 2, ,P}for some P is an element of N-w0 := {w(0), w(0) + 1, w(0 )+ 2,...}. The numerical part of the paper is dedicated to examinin the validity of the setsH(k,E)and M-k,M-E for different values of k and E. For this reason, we illustrate the domain of solutions via several figures explaining the validity of the main theorem.