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

نویسندگان
Alsadi, Wadhah Ahmed ID 1
Abdullah, Tariq Q. S. ID 2
Hussein, Mokhtar ID 3

1 School of Mathematics and Physics, China University of Geosciences(Wuhan), Wuhan, China

2 School of Mathematics and Physics, China University of Geosciences(Wuhan), Wuhan, China.

3 School of Mechanical Engineering and Automation, Northeastern University, Shenyang, China.

doi
10.22034/cmde.2021.32807.1580
چکیده

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 − 1 < σ, ϵ ≤ k, and k ≥ 3. 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.

کلیدواژه‌ها
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)