Stability analysis of a nonlinear coupled implicit switched singular fractional differential system with p-Laplacian

This paper deals with existence, uniqueness, and Hyers–Ulam stability of solutions to a nonlinear coupled implicit switched singular fractional differential system involving Laplace operator $\phi _{p}$ ϕ p . The proposed problem consists of two kinds of fractional derivatives, that is, Riemann–Liouville fractional derivative of order β and Caputo fractional derivative of order σ, where $m-1<\beta $ m − 1 < β , $\sigma < m$ σ < m , $m\in \{2,3,\dots \}$ m ∈ { 2 , 3 , … } . Prior to proceeding to the main results, the system is converted into an equivalent integral form by the help of Green’s function. Using Schauder’s fixed point theorem and Banach’s contraction principle, the existence and uniqueness of solutions are proved. The main results are demonstrated by an example.