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Citation - WoS: 14
Citation - Scopus: 19
On the Discrete Sumudu Transform
(Editura Acad Romane, 2012) Jarad, Fahd; Jarad, Fahd; Abdeljawad, Thabet; Bayram, Kamm; Abdeljawad, Thabet; Baleanu, Dumitru; Baleanu, Dumitru; Köse, Hasan; Ameen, Raad; Matematik
In this paper, we define the Sumudu transform on an arbitrary time scale. Starting from this definition we define the discrete Sumudu transform. We prove the initial and final value problems and study the basic properties of this transform. We also present the discrete Sumudu transform of some basic functions.
Citation - WoS: 45
Citation - Scopus: 51
Ulam Stability for Delay Fractional Differential Equations With a Generalized Caputo Derivative
(Univ Nis, Fac Sci Math, 2018) Abdeljawad, Thabet; Ameen, Raad; Jarad, Fahd
The objective of this paper is to extend Ulam-Hyers stability and Ulam-Hyers-Rassias stability theory to differential equations with delay and in the frame of a certain class of a generalized Caputo fractional derivative with dependence on a kernel function. We discuss the conditions such delay generalized Caputo fractional differential equations should satisfy to be stable in the sense of Ulam-Hyers and Ulam-Hyers-Rassias. To demonstrate our results two examples are presented.

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