Hilfer-Hadamard-Type Fractional Differential Equation with Cauchy-Type Problem
Analysis of PDEs
2018-02-22 v1
Abstract
In this paper, we consider the Cauchy-type problem (1.1) involving Hilfer-Hadamard-type fractional derivative for a nonlinear fractional differential equation. We prove an equivalence between the Cauchy-type problem (1.1) and Volterra integral equation(VIE), existence, and uniqueness. We present a slight generalization for the Gronwall inequality which was used in studying the continuous dependence of a solution for the Cauchy-type problem (1.2).
Cite
@article{arxiv.1802.07483,
title = {Hilfer-Hadamard-Type Fractional Differential Equation with Cauchy-Type Problem},
author = {Ahmad Y. A. Salamooni and D. D. Pawar},
journal= {arXiv preprint arXiv:1802.07483},
year = {2018}
}
Comments
18 pages