Caputo-Katugampola fractional Volterra functional differential equations with a vanishing lag function
Volume 13, Issue 5, pp 293--302
http://dx.doi.org/10.22436/jnsa.013.05.06
Publication Date: March 29, 2020
Submission Date: October 14, 2019
Revision Date: February 11, 2020
Accteptance Date: February 15, 2020
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Authors
M. I. Youssef
- 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.
Abstract
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.
Share and Cite
ISRP Style
M. I. Youssef, Caputo-Katugampola fractional Volterra functional differential equations with a vanishing lag function, Journal of Nonlinear Sciences and Applications, 13 (2020), no. 5, 293--302
AMA Style
Youssef M. I., Caputo-Katugampola fractional Volterra functional differential equations with a vanishing lag function. J. Nonlinear Sci. Appl. (2020); 13(5):293--302
Chicago/Turabian Style
Youssef, M. I.. "Caputo-Katugampola fractional Volterra functional differential equations with a vanishing lag function." Journal of Nonlinear Sciences and Applications, 13, no. 5 (2020): 293--302
Keywords
- Volterra functional equation
- existence
- uniqueness
- fixed point principle
- delay function
MSC
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