Siberian Federal University 
- Issue
- Journal of Siberian Federal University. Mathematics & Physics. 2021 14 (2)
- Authors
- Almalahi, Mohammed A.; Panchal, Satish K.
- Contact information
- Almalahi, Mohammed A.: Department of Mathematics Dr. Babasaheb Ambedkar Marathwada University Aurangabad (M.S), India; OCRID: 0000-0001-5719-086X; Panchal, Satish K.: Department of Mathematics Dr. Babasaheb Ambedkar Marathwada University Aurangabad (M.S), India;
- Keywords
- fractional differential equations; fractional derivatives; Eα -Ulam-Hyers stability; fixed point theorem
- Abstract
In this paper, we derive the representation formula of the solution for ψ-Hilfer fractional differential equation with constant coefficient in the form of Mittag-Leffler function by using Picard’s successive approximation. Moreover, by using some properties of Mittag-Leffler function and fixed point theorems such as Banach and Schaefer, we introduce new results of some qualitative properties of solution such as existence and uniqueness. The generalized Gronwall inequality lemma is used in analyze Eα -Ulam-Hyers stability. Finally, one example to illustrate the obtained results
- Pages
- 159–175
- DOI
- 10.17516/1997-1397-2021-14-2-161-177
- Paper at repository of SibFU
- https://elib.sfu-kras.ru/handle/2311/137965
Journal of Siberian Federal University. Mathematics & Physics / On the Theory of ψ-Hilfer Nonlocal Cauchy Problem
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