Existence results for systems of conformable fractional differential equations

Bouharket Bendouma, Alberto Cabada, and Ahmed Hammoudi

Address:
Ibn Khaldoun, Tiaret University, P.O. Box 78, 14000 Zaâroura, Tiaret, Algeria University of Sidi Bel Abbès, P.O. Box 89, Sidi Bel Abbès, 22000, Algeria
Instituto de Matemáticas, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, Galicia, Spain
Laboratory of Mathematics, Ain Témouchent University, P.O. Box 89, 46000 Ain Témouchent, Algeria

E-mail:
bendouma73@gmail.com
alberto.cabada@usc.es
hymmedahmed@gmail.com

Abstract: In this article, we study the existence of solutions to systems of conformable fractional differential equations with periodic boundary value or initial value conditions. where the right member of the system is $L^{1}_{\alpha }$-carathéodory function. We employ the method of solution-tube and Schauder’s fixed-point theorem.

AMSclassification: primary 34A08; secondary 26A33, 34A34, 34A12, 34K37, 34B15.

Keywords: conformable fractional calculus, conformable fractional differential equations, solution-tube, Schauder’s fixed-point theorem, fractional Sobolev’s spaces.

DOI: 10.5817/AM2019-2-69