Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
Browse
13 results
Search Results
Article Citation - WoS: 144Citation - Scopus: 158Semi-Analytical Study of Pine Wilt Disease Model With Convex Rate Under Caputo-Febrizio Fractional Order Derivative(Pergamon-elsevier Science Ltd, 2020) Jarad, Fahd; Abdeljawad, Thabet; Shah, Kamal; Alqudah, Manar A.In this paper, we present semi-analytical solution to Pine Wilt disease (PWD) model under the CaputoFabrizio fractional derivative (CFFD). For the proposed solution, we utilize Laplace transform coupled with Adomian decomposition method abbreviated as (LADM). The concerned method is a powerful tool to obtain semi-analytical solution for such type of nonlinear differential equations of fractional order (FODEs) involving non-singular kernel. Furthermore, we give some results for the existence of solution to the proposed model and present numerical results to verify the established analysis. (C) 2020 Elsevier Ltd. All rights reserved.Article Citation - WoS: 41Citation - Scopus: 46Existence of Positive Solutions for Weighted Fractional Order Differential Equations(Pergamon-elsevier Science Ltd, 2020) Ali, Saeed M.; Shah, Kamal; Jarad, Fahd; Abdo, Mohammed S.; Abdeljawad, ThabetIn this paper, we deliberate two classes of initial value problems for nonlinear fractional differential equations under a version weighted generalized of Caputo fractional derivative given by Jarad et al. (2020a) [25]. We get a formula for the solution through the equivalent fractional integral equations to the proposed problems. The existence and uniqueness of positive solutions have been obtained by using lower and upper solutions. The acquired results are demonstrated by building the upper and lower control functions of the nonlinear term with the aid of Banach and Schauder fixed point theorems. The acquired results are demonstrated by pertinent numerical examples along with the Bashforth Moulton prediction correction scheme and Matlab. (C) 2020 Elsevier Ltd. All rights reserved.Article Citation - WoS: 77Citation - Scopus: 83A Singular Abc-Fractional Differential Equation With P-Laplacian Operator(Pergamon-elsevier Science Ltd, 2019) Abdeljawad, Thabet; Khan, Aziz; Khan, Hasib; Jarad, FahdIn this article, we have focused on the existence and uniqueness of solutions and Hyers-Ulam stability for ABC-fractional DEs with p-Laplacian operator involving spatial singularity. The existence and uniqueness of solutions are derived with the help of the well-known Guo-Krasnoselskii theorem. Our work is a continuation of the study carried out in the recently published article " Chaos Solitons & Fractals. 2018;117:16-20." To manifest the results, we include an example with specific parameters and assumptions. (C) 2019 Elsevier Ltd. All rights reserved.Article Citation - WoS: 34Citation - Scopus: 37Monotonicity Analysis for Nabla H-Discrete Fractional Atangana-Baleanu Differences(Pergamon-elsevier Science Ltd, 2018) Jarad, Fahd; Suwan, Iyad; Abdeljawad, ThabetIn this article, benefiting from the nabla h-fractional functions and nabla h-Taylor polynomials, some properties of the nabla h-discrete version of Mittag-Leffler (h-ML) function are studied. The monotonicity of the nabla h-fractional difference operator with h-ML kernel (Atangana-Baleanu fractional differences) is discussed. As an application, the Mean Value Theorem (MVT) on hZ is proved. (C) 2018 Elsevier Ltd. All rights reserved.Article Citation - WoS: 321Citation - Scopus: 350On a Class of Ordinary Differential Equations in the Frame of Atangana-Baleanu Fractional Derivative(Pergamon-elsevier Science Ltd, 2018) Jarad, Fahd; Abdeljawad, Thabet; Hammouch, ZakiaIn this paper, we discuss the conditions of existence and uniqueness of solutions to a certain class of ordinary differential equations involving Atangana-Baleanu fractional derivative. Benefiting from the Gronwall inequality in the frame of Riemann-Liouville fractional integral, we establish a Gronwall inequality in the frame of Atangana-Baleanu fractional integral. Then, we study the stability of such equations in the sense of Ulam. (C) 2018 Elsevier Ltd. All rights reserved.Article Citation - WoS: 235Citation - Scopus: 257On Fractional Derivatives With Exponential Kernel and Their Discrete Versions(Pergamon-elsevier Science Ltd, 2017) Abdeljawad, Thabet; Baleanu, DumitruIn this paper we define the right fractional derivative and its corresponding right fractional integral with exponential kernel. We provide the integration by parts formula and we use the Q-operator to confirm our results. The related Euler Lagrange equations are obtained and one example is reported. Moreover, we formulate and discuss the discrete counterparts of our results.Article Citation - WoS: 87Citation - Scopus: 80Monotonicity Analysis of a Nabla Discrete Fractional Operator With Discrete Mittag-Leffler Kernel(Pergamon-elsevier Science Ltd, 2017) Abdeljawad, Thabet; Baleanu, DumitruDiscrete fractional calculus is one of the new trends in fractional calculus both from theoretical and applied viewpoints. In this article we prove that if the nabla fractional difference operator with discrete Mittag-Leffler kernel ((ABR)(a -1) del(alpha)y) (t) of order 0 < alpha < 1/2 and starting at a - 1 is positive, then y(t) is alpha(2)- increasing. That is y (t + 1) >= alpha(2)y(t) for all t is an element of N-a = {a, a + 1,...}. Conversely, if y(t) is increasing and y(a) >= 0, then ((ABR)(a-1)del(alpha)y)(t) >= 0. The monotonicity properties of the Caputo and right fractional differences are concluded as well. As an application, we prove a fractional difference version of mean-value theorem. Finally, some comparisons to the classical discrete fractional case and to fractional difference operators with discrete exponential kernel are made. (C) 2017 Elsevier Ltd. All rights reserved.Article Citation - WoS: 112Citation - Scopus: 134Fractional Logistic Models in the Frame of Fractional Operators Generated by Conformable Derivatives(Pergamon-elsevier Science Ltd, 2019) Jarad, Fahd; Abdeljawad, Thabet; Al-Mdallal, Qasem M.In this article, we study different types of fractional-order logistic models in the frame of Caputo type fractional operators generated by conformable derivatives (Caputo CFDs). We present the existence and uniqueness theorems to solutions of these models and discuss their stability by perturbing the equilibrium points. Finally, we furniture our results by illustrative numerical examples for the studied models. (C) 2018 Elsevier Ltd. All rights reserved.Article Citation - WoS: 90Citation - Scopus: 94Stability of Q-Fractional Non-Autonomous Systems(Pergamon-elsevier Science Ltd, 2013) Jarad, Fahd; Abdeljawad, Thabet; Baleanu, DumitruIn this manuscript, using Lyapunov's direct method, the stability of non-autonomous systems within the frame of the q-Caputo fractional derivative is studied. The conditions for stability, uniform stability and asymptotic stability are discussed. (C) 2012 Elsevier Ltd. All rights reserved.Article Citation - WoS: 79Citation - Scopus: 82A Generalized Contraction Principle With Control Functions on Partial Metric Spaces(Pergamon-elsevier Science Ltd, 2012) Abdeljawad, Thabet; Karapinar, Erdal; Tas, KenanPartial metric spaces were introduced by Matthews in 1994 as a part of the study of denotational semantics of data flow networks. In this article, we prove a generalized contraction principle with control functions phi and psi on partial metric spaces. The theorems we prove generalize many previously obtained results. We also give some examples showing that our theorems are indeed proper extensions. (C) 2011 Elsevier Ltd. All rights reserved.