Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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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: 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: 3Citation - Scopus: 3Monotonicity and Extremality Analysis of Difference Operators in Riemann-Liouville Family(Amer inst Mathematical Sciences-aims, 2023) Abdeljawad, Thabet; Al-Sarairah, Eman; Hamed, Y. S.; Mohammed, Pshtiwan Othman; Baleanu, DumitruIn this paper, we will discuss the monotone decreasing and increasing of a discrete nonpositive and nonnegative function defined on Nr0+1, respectively, which come from analysing the discrete Riemann-Liouville differences together with two necessary conditions (see Lemmas 2.1 and 2.3). Then, the relative minimum and relative maximum will be obtained in view of these results combined with another condition (see Theorems 2.1 and 2.2). We will modify and reform the main two lemmas by replacing the main condition with a new simpler and stronger condition. For these new sufficient for the function to be monotone decreasing or increasing.Article Citation - WoS: 12Citation - Scopus: 15Variational Principles in the Frame of Certain Generalized Fractional Derivatives(Amer inst Mathematical Sciences-aims, 2020) Jarad, Fahd; Abdeljawad, ThabetIn this article, we study generalized fractional derivatives that contain kernels depending on a function on the space of absolute continuous functions. We generalize the Laplace transform in order to be applicable for the generalized fractional integrals and derivatives and apply this transform to solve some ordinary differential equations in the frame of the fractional derivatives under discussion.Article Citation - WoS: 4Citation - Scopus: 4Nonlinear Singular P-Laplacian Boundary Value Problems in the Frame of Conformable Derivative(Amer inst Mathematical Sciences-aims, 2021) Jarad, Fahd; Adjabi, Yassine; Abdeljawad, Thabet; Bouloudene, Mokhtar; Alqudah, Manar A.This paper studies a class of fourth point singular boundary value problem of p-Laplacian operator in the setting of a specific kind of conformable derivatives. By using the upper and lower solutions method and fixed point theorems on cones., necessary and sufficient conditions for the existence of positive solutions are obtained. In addition, we investigate the dependence of the solution on the order of the conformable differential equation and on the initial conditions.Article Citation - WoS: 7Citation - Scopus: 9Mathematical Study of Sir Epidemic Model Under Convex Incidence Rate(Amer inst Mathematical Sciences-aims, 2020) Alqudah, Manar A.; Abdeljawad, Thabet; Jarad, Fahd; Din, Rahim Ud; Shah, KamalIn this manuscript, we examine the SIR model under convex incidence rate. We first formulate the famous SIR model under the aforesaid incidence rate. Further, we develop some sufficient analysis to examine the dynamical behavior of the model under consideration. We compute the basic reproductive number R-0: Also we study the global attractivity results via using Dulac function theory. Further, we also provide some information about the stability of the endemic and disease free equilibria for the considered model. In addition, we use nonstandard finite difference scheme to perform numerical simulation of the considered model via using Matlab. We provide different numerical plots for two different values of contact rate and taking various initial values for compartments involved in the considered model.Article Citation - WoS: 8Citation - Scopus: 10Lyapunov Type Inequality in the Frame of Generalized Caputo Derivatives(Amer inst Mathematical Sciences-aims, 2021) Abdeljawad, Thabet; Mallak, Saed F.; Alrabaiah, Hussam; Jarad, Fahd; Adjabi, YassineIn this paper, we establish the Lyapunov-type inequality for boundary value problems involving generalized Caputo fractional derivatives that unite the Caputo and Caputo-Hadamrad fractional derivatives. An application about the zeros of generalized types of Mittag-Leffler functions is given.Article Citation - WoS: 390Citation - Scopus: 406Generalized Fractional Derivatives and Laplace Transform(Amer inst Mathematical Sciences-aims, 2020) Jarad, Fahd; Abdeljawad, ThabetIn this article, we study generalized fractional derivatives that contain kernels depending on a function on the space of absolute continuous functions. We generalize the Laplace transform in order to be applicable for the generalized fractional integrals and derivatives and apply this transform to solve some ordinary differential equations in the frame of the fractional derivatives under discussion.