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 : 15 | Download : 5

Publication Date : 2020-12-30

Article Type : Research Paper

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