Volume 42_1_(2021)_35-48

New existence results for fractional differential equations in a weighted Sobolev space
Ahmed Hallaci, Hamid Boulares, Abdelouaheb Ardjouni, Abderrazak Chaoui

Abstract. In this paper, we give some conditions to prove the existence of solutions for a nonlinear boundary value problem of fractional differential equations with higher order q, (n-1< q<n), involving Riemann-Liouville fractional derivative. The solutions are discussed in a weighted fractional Riemann-Liouville Sobolev space using Schauder's fixed point theorem. An example is given to illustrate the main results.

Rend. Mat. Appl. (7) 42 (2021) 35-48;  pdf