Sequential fractional differential equations and unification of anti-periodic and multi-point boundary conditions

Alsaedi, Ahmed¹ ; Ahmad, Bashir¹ ; Aqlan, Mohammed¹

¹ Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 1, p. 71-83.

Résumé

In this paper, we present a novel idea of unification of anti-periodic and multi-point boundary conditions and develop the existence theory for sequential fractional differential equations supplemented with these new conditions. We apply fixed point theorems due to Banach, Krasnoselskii, Leray-Schauder alternative criterion, and Leray-Schauder degree theory to obtain the desired results. Our results are well-illustrated with the aid of examples and correspond to some new special cases for particular choices of parameters involved in the problem.

Détail

DOI : 10.22436/jnsa.010.01.07

Classification : 34A08, 34B10, 34B15
Keywords: Sequential fractional differential equations, nonlocal, anti-periodic, multi-point, existence, fixed point.

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