Fractional ${q}$-difference equations on the half line

Saïd Abbas a, Mouffak Benchohra b,c, Nadjet Laledj b, and Yong Zhou d

Address:
a Department of Mathematics, Tahar Moulay University of Saïda, P.O. Box 138, EN-Nasr, 20000 Saïda, Algeria
b Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, P.O. Box 89, Sidi Bel-Abbès 22000, Algeria
c Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
d Faculty of Mathematics and Computational Science, Xiangtan University, Hunan 411105, P.R. China

E-mail:
abbasmsaid@yahoo.fr
benchohra@yahoo.com

Abstract: This article deals with some results about the existence of solutions and bounded solutions and the attractivity for a class of fractional ${q}$-difference equations. Some applications are made of Schauder fixed point theorem in Banach spaces and Darbo fixed point theorem in Fréchet spaces. We use some technics associated with the concept of measure of noncompactness and the diagonalization process. Some illustrative examples are given in the last section.

AMSclassification: primary 26A33.

Keywords: fractional q-difference equation, attractivity, diagonalization, bounded solution, Banach space, Fréchet space, fixed point.

DOI: 10.5817/AM2020-4-207