English

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).

Keywords

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

R2 v1 2026-06-23T00:28:36.146Z