Hilfer-Hadamard-Type Fractional Differential Equation with Cauchy-Type Problem

2018/02/21 by Ahmad Y. A. Salamooni, Salamooni, Ahmad Y. A., D. D. Pawar +1
Mathematics · #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.1802.07483

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).

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