On existence and stability results to a class of boundary value problems under Mittag-Leffler power law

Abstract

Abstract Some essential conditions for existence theory and stability analysis to a class of boundary value problems of fractional delay differential equations involving Atangana–Baleanu-Caputo derivative are established. The deserted results are derived by using the Banach contraction and Krasnoselskii’s fixed point theorems. Moreover, different kinds of stability theory including Hyers–Ulam, generalized Hyers–Ulam, Hyers–Ulam-Rassias and generalized Hyers–Ulam–Rassias stability are also developed for the problem under consideration. Appropriate examples are given for illustrative purposes.

Keywords

• Boundary conditions
• ABC fractional derivative
• Krasnoselskii fixed point theorem
• Stability theory