Existence and stability criterion for the results of fractional order Φp-Laplacian operator boundary value problem

In this literature, we study the existence and stability of the solution of the boundary value problem of fractional differential equations with Φp-Laplacian operator. Our problem is based on Caputo fractional derivative of orders σ, ϵ, where k − ۱ < σ, ϵ ≤ k, and k ≥ ۳. By using the Schauder fixed point theory and properties of the Green function, some conditions are established which show the criterion of the existence and non-existence solution for the proposed problem. We also investigate some adequate conditions for the Hyers-Ulam stability of the solution. Illustrated examples are given as an application of our result.

Keywords:

Fractional differential equations(FDEs) , Caputo factional derivative , Boundary value problem(BVP) , Schauder fixed point , Hyers-Ulams(UH) stability , Existence and uniqueness(EUS) , Laplacian operator , Differential equations(DEs)