Continuous dependence solutions for Hilfer fractional differential equations with nonlocal conditions

Abbas, Mohamed I.¹

¹ Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria 21511, Egypt

Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 9, p. 573-581.

Résumé

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.

Détail

DOI : 10.22436/jnsa.012.09.02

Classification : 26A33, 34A08, 34A12
Keywords: Hilfer fractional derivative, Krasnoselskii's fixed point theorem, Gronwall's inequality

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