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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.
Citation - WoS: 63
Citation - Scopus: 74
On Generalized Fractional Operators and a Gronwall Type Inequality With Applications
(Univ Nis, Fac Sci Math, 2017) Abdeljawad, Thabet; Adjabi, Yassine; Jarad, Fahd
In this paper, we obtain the Gronwall type inequality for generalized fractional operators unifying Riemann-Liouville and Hadamard fractional operators. We apply this inequality to the dependence of the solution of differential equations, involving generalized fractional derivatives, on both the order and the initial conditions. More properties for the generalized fractional operators are formulated and the solutions of initial value problems in certain new weighted spaces of functions are established as well.

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