S K Panchal | Searcharxiv

arXiv2019

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

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 $ψ$-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.

math.GM↗

arXiv2019

Existence of solution for Hilfer fractional differential equations with boundary value conditions

In this paper, we consider a class of nonlinear fractional differential equations involving Hilfer derivative with boundary conditions. First, we obtain an equivalent integral for the given boundary value problem in weighted space of continuous functions. Then we obtain the existence results for a given problem under a new approach and minimal assumptions on nonlinear function f. The technique used in the analysis relies on a variety of tools including Schauder, Schaefer and Krasnoselski fixed point theorems. We demonstrate our results through illustrative examples.

math.GM↗