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

Authors : Zeeshan ALİ, Akbar ZADA, Kamal SHAH

Pages : 1092-1109

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Publication Date : 2019-08-08

Article Type : Research Paper

Abstract :In this manuscript, we study the existence and uniqueness of solution for a class of fractional order boundary value problem insert ignore into journalissuearticles values(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