Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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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: 16Citation - Scopus: 19Qualitative Analysis of Implicit Dirichlet Boundary Value Problem for Caputo-Fabrizio Fractional Differential Equations(Hindawi Ltd, 2020) Shah, Kamal; Abdeljawad, Thabet; Jarad, Fahd; Gul, Rozi; Sarwar, MuhammadThis article studies a class of implicit fractional differential equations involving a Caputo-Fabrizio fractional derivative under Dirichlet boundary conditions (DBCs). Using classical fixed-point theory techniques due to Banch's and Krasnoselskii, a qualitative analysis of the concerned problem for the existence of solutions is established. Furthermore, some results about the stability of the Ulam type are also studied for the proposed problem. Some pertinent examples are given to justify the results.Article Citation - WoS: 86Qualitative Analysis of a Mathematical Model in the Time of Covid-19(Hindawi Ltd, 2020) Mahariq, Ibrahim; Jarad, Fahd; Shah, Kamal; Abdeljawad, ThabetIn this article, a qualitative analysis of the mathematical model of novel corona virus named COVID-19 under nonsingular derivative of fractional order is considered. The concerned model is composed of two compartments, namely, healthy and infected. Under the new nonsingular derivative, we, first of all, establish some sufficient conditions for existence and uniqueness of solution to the model under consideration. Because of the dynamics of the phenomenon when described by a mathematical model, its existence must be guaranteed. Therefore, via using the classical fixed point theory, we establish the required results. Also, we present the results of stability of Ulam's type by using the tools of nonlinear analysis. For the semianalytical results, we extend the usual Laplace transform coupled with Adomian decomposition method to obtain the approximate solutions for the corresponding compartments of the considered model. Finally, in order to support our study, graphical interpretations are provided to illustrate the results by using some numerical values for the corresponding parameters of the model.Article Citation - WoS: 8Citation - Scopus: 11Mathematical Analysis of Nonlocal Implicit Impulsive Problem Under Caputo Fractional Boundary Conditions(Hindawi Ltd, 2020) Abdeljawad, Thabet; Shah, Kamal; Jarad, Fahd; Ali, Arshad; Gupta, VidushiThis paper is related to frame a mathematical analysis of impulsive fractional order differential equations (IFODEs) under nonlocal Caputo fractional boundary conditions (NCFBCs). By using fixed point theorems of Schaefer and Banach, we analyze the existence and uniqueness results for the considered problem. Furthermore, we utilize the theory of stability for presenting Hyers-Ulam, generalized Hyers-Ulam, Hyers-Ulam-Rassias, and generalized Hyers-Ulam-Rassias stability results of the proposed scheme. Finally, some applications are offered to demonstrate the concept and results. The whole analysis is carried out by using Caputo fractional derivatives (CFDs).Article Citation - WoS: 5Citation - Scopus: 5Generalized Darbo-Type F-Contraction and F-Expansion and Its Applications To a Nonlinear Fractional-Order Differential Equation(Hindawi Ltd, 2020) Abdeljawad, Thabet; Jarad, Fahd; Zada, Mian Bahadur; Sarwar, MuhammadIn this work, we introduce various Darbo-type F -contractions pound, and utilizing these contractions, we present some fixed point theorems. Moreover, we introduce a Darbo-type F -expanding pound mapping and prove fixed point theorems under the Darbo-type F -expanding pound mapping. Employing our results, we check the existence of a solution to the nonlinear fractional-order differential equation under the integral type boundary conditions. For its validity, an appropriate example is given.Article Citation - WoS: 27Citation - Scopus: 29Existence and Uniqueness of Uncertain Fractional Backward Difference Equations of Riemann-Liouville Type(Hindawi Ltd, 2020) Jarad, Fahd; Chu, Yu-Ming; Mohammed, Pshtiwan Othman; Abdeljawad, ThabetIn this article, we consider the analytic solutions of the uncertain fractional backward difference equations in the sense of Riemann-Liouville fractional operators which are solved by using the Picard successive iteration method. Also, we consider the existence and uniqueness theorem of the solution to an uncertain fractional backward difference equation via the Banach contraction fixed-point theorem under the conditions of Lipschitz constant and linear combination growth. Finally, we point out some examples to confirm the validity of the existence and uniqueness of the solution.Article Citation - WoS: 3Certain Subclasses of Β-Uniformly Q-Starlike and Β-Uniformly Q-Convex Functions(Hindawi Ltd, 2020) Abdeljawad, Thabet; Jarad, Fahd; AbuJarad, Eman S. A.; AbuJarad, Mohammed H. A.In this paper, the authors introduced certain subclasses beta-uniformly q-starlike and beta-uniformly q-convex functions of order a involving the q-derivative operator defined in the open unit disc. Coefficient bounds were also investigated.Editorial Citation - WoS: 1Citation - Scopus: 1Recent Developments and Applications on Discrete Fractional Equations and Related Topics(Hindawi Ltd, 2013) Alzabut, Jehad; Sun, Shurong; Abdeljawad, ThabetArticle Citation - WoS: 3Citation - Scopus: 2Perron-Type Criterion for Linear Difference Equations With Distributed Delay(Hindawi Ltd, 2007) Alzabut, Jehad O.; Abdeljawad, ThabetIt is shown that if a linear difference equation with distributed delay of the form Delta x(n) = Sigma(0)(k=-d)Delta(k)zeta(n + 1, k - 1)x(n + k - 1), n >= 1, satisfies a Perron condition then its trivial solution is uniformly asymptotically stable. Copyright (c) 2007 J. O. Alzabut and T. Abdeljawad. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Article Citation - WoS: 142Citation - Scopus: 170On Delta and Nabla Caputo Fractional Differences and Dual Identities(Hindawi Ltd, 2013) Abdeljawad, ThabetWe investigate two types of dual identities for Caputo fractional differences. The first type relates nabla and delta type fractional sums and differences. The second type represented by the Q-operator relates left and right fractional sums and differences. Two types of Caputo fractional differences are introduced; one of them (dual one) is defined so that it obeys the investigated dual identities. The relation between Riemann and Caputo fractional differences is investigated, and the delta and nabla discrete Mittag-Leffler functions are confirmed by solving Caputo type linear fractional difference equations. A nabla integration by parts formula is obtained for Caputo fractional differences as well.