Caputo-Katugampola fractional Volterra functional differential equations with a vanishing lag function

Youssef, M. I. ¹

¹ Department of Mathematics, College of Science, Jouf University, P. O. Box 2014, Sakaka, Saudi Arabia;Department of Mathematics, Faculty of Education, Alexandria University, Alexandria, Egypt

Journal of nonlinear sciences and its applications, Tome 13 (2020) no. 5, p. 293-302.

Résumé

In the present article, we study the solvability of a class of fractional functional integro-differential equations of the Caputo-Katugampola type. The existence of solutions is investigated under sufficient conditions as well as the assumptions which guarantee the uniqueness of the solution is explained. Also, we examine the continuous dependence of the solution on the initial condition, the lag function $0 \leq \psi(t)\leq t$, and the considered nonlinear functional. We give an example to explain our results. The outcomes in this paper extend the results developed by El-Sayed et al. in [A. M. A. El-Sayed, R. G. Ahmed, J. Nonlinear Sci. Appl., $\bf 13$ (2020), 1--8], recently.

Détail

DOI : 10.22436/jnsa.013.05.06

Classification : 34A12, 45D99, 34K37
Keywords: Volterra functional equation, existence, uniqueness, fixed point principle, delay function

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