Stability analysis of implicit fractional differential equation with anti–periodic integral boundary value problem

Akbar Zada, Hira Waheed
2020 Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica  
In this manuscript, we study the existence, uniqueness and various kinds of Ulam stability including Ulam–Hyers stability, generalized Ulam–Hyers stability, Ulam–Hyers–Rassias stability, and generalized Ulam–Hyers– Rassias stability of the solution to an implicit nonlinear fractional differential equations corresponding to an implicit integral boundary condition. We develop conditions for the existence and uniqueness by using the classical fixed point theorems such as Banach contraction
more » ... e and Schaefer's fixed point theorem. For stability, we utilize classical functional analysis. The main results are well illustrated with an example.
doi:10.2478/aupcsm-2020-0001 fatcat:4moqgsr24jfctfmboosw5fj4ca