Abstract

In this paper, we investigate the existence and uniqueness results for the solutions to implicit fractional differential equations involving generalized Katugampola derivative with nonlocal initial condition. By means of some classical fixed point theorem techniques such as Krasnosel'skii fixed point theorem and Banach contraction principle we established our main results. A suitable example is given to illustrate the applicability of our main results.

Keywords and Phrases

Generalized Katugampola derivative, implicit differential equation, existence, Uniqueness, fixed point.

A.M.S. subject classification

26A33, 34A08, 34A12.

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