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arXiv · 1802.07483

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

Ahmad Y. A. Salamooni·D. D. Pawar
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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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Ahmad Y. A. Salamooni, D. D. Pawar. 2018-02-21. Hilfer-Hadamard-Type Fractional Differential Equation with Cauchy-Type Problem. https://arxiv.org/abs/1802.07483

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