# Continuous dependence solutions for Hilfer fractional differential equations with nonlocal conditions

Volume 12, Issue 9, pp 573--581 Publication Date: April 17, 2019       Article History
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### Authors

Mohamed I. Abbas - Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria 21511, Egypt.

### Abstract

We discuss the existence, uniqueness and continuous dependence of solution for a non-autonomous semilinear Hilfer fractional differential equation with nonlocal conditions in the space of weighted continuous functions. By means of the Krasnoselskii's fixed point theorem and the generalized Gronwall's inequality, we establish the desired results.

### Keywords

• Hilfer fractional derivative
• Krasnoselskii's fixed point theorem
• Gronwall's inequality

•  26A33
•  34A08
•  34A12

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