- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 4 Issue: 4
- Existence and stability results of relaxation fractional differential equations with Hilfer--Katugam...
Existence and stability results of relaxation fractional differential equations with Hilfer--Katugampola fractional derivative.
Authors : Mohammed Almalahi, Satish K. Panchal
Pages : 299-315
Doi:10.31197/atnaa.686693
View : 5 | Download : 2
Publication Date : 2020-12-30
Article Type : Research
Abstract :In this work, we present the existence, uniqueness, and stability result of solution to the nonlinear fractional differential equations involving Hilfer-Katugampola derivative subject to nonlocal fractional integral bound- ary conditions. The reasoning is mainly based upon properties of Mittag-Leffler functions, and fixed-point methods such as Banach contraction principle and Krasnoselskii's fixed point theorem. Moreover, the gener- alized Gornwall inequality lemma is used to analyze different types of stability. Finally, one example is given to illustrate our theoretical results.Keywords : Hilfer--Katugampola fractional derivative, Existence, Mittag-Leffler functions, Ulam stability