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arXiv · 1909.13681

On existence of solution to nonlinear $\psi$-Hilfer Cauchy-type problem

Mohammed S Abdo·S K Panchal·Sandeep P Bhairat
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Abstract

The aim of this paper is to obtain the existence of unique solution to nonlinear Cauchy-type problem. We consider the implicit nonlinear Cauchy-type problem with $\psi$-Hilfer fractional derivative. The Banach fixed point theorem is used to obtain the existence of a unique solution whereas the generalized Gronwall inequality is used to discuss continuous data dependence of the solution. The results obtained herein are supported with illustrative example.

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Mohammed S Abdo, S K Panchal, Sandeep P Bhairat. 2019-09-26. On existence of solution to nonlinear $\psi$-Hilfer Cauchy-type problem. https://arxiv.org/abs/1909.13681

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