Investigating a Class of Nonlinear Fractional Differential Equations and Its Hyers-Ulam Stability by Means of Topological Degree Theory

Abstract

The aim of this article is to seek some adequate conditions via a prior estimate method (topological degree method) to derive the existence of solution to a nonlinear boundary value problem of fractional differential equations (FDEs). With the help of topological degree method which has been applied in many articles, we establish the required results for existence and uniqueness of solution to a class of FDEs. Moreover, we also formulate sufficient conditions for Hyers-Ulam stability to the solution of the considered problem. Finally, an appropriate example is provided to justify the relevant results.

Keywords:

• Boundary conditions
• fractional differential equations
• Hyers-Ulam type stability

Mathematics subject classification:

• 26A33
• 34A08
• 34B27
• 35B40

Acknowledgments

We are thankful to the reviewers for their useful comments which improved this article very well.

Additional information

Funding

We remark that this work has been financially supported by the HEC of Pakistan, Grant No: 10039/KPK/NRPU/R&D/HEC/2017 and HED of KPK, Government of Pakistan at Grant No: HEREF-46.