EXISTENCE OF MILD SOLUTIONS FOR ATANGANA-BALEANU RETARDED FRACTIONAL DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

Resumen

In the present paper, we investigate the existence of mild solutions for retarded semilinear fractional differential equations subject to nonlocal conditions in a Banach space. The results are obtained by applying the Schauder fixed point theorem and Gr¨onwall’s inequality, under suitable assumptions. Finally, an example is provided to illustrate and justify the theoretical results.