Ulam stability results for the solutions of nonlinear implicit fractional order differential equations

Abstract

In this manuscript, we study the existence and uniqueness of solution for a class of fractional order boundary value problem (FBVP) for implicit fractional differential equations with Riemann-Liouville derivative. Furthermore, we investigate different kinds of Ulam stability such as Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for the proposed problem. The concerned analysis is carried out through using classical technique of nonlinear functional analysis. The main results are illustrated by providing a couple of examples

Keywords

• Riemann-Liouville fractional derivative,implicit fractional differential equations,existence,Green function,Ulam-Hyers stability

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