Some Results on Fractional Differential Equation With Mixed Boundary Condition via S-Iteration - Tidke, Haribhau L.; Patil, Gajanan S. (Communications in Mathematics and Applications, 2022)
The present paper discuss the existence, uniqueness and other properties of solutions of nonlinear differential equation of fractional order involving the Caputo fractional derivative with mixed boundary condition. The analysis of obtained results is based on application of S-iteration method. Since the study of qualitative properties in general required differential and integral inequalities, but here S-iteration method itself has equally important contribution to study various properties such as dependence on boundary data, closeness of solutions and dependence on parameters and functions involved therein. The results obtained are illustrated through example.
Keywords: Existence and uniqueness; S-iterative method; Fractional derivative; Continuous dependence; Closeness; Parameters; Boundary value problem