Sequential Caputo–Hadamard Fractional Differential Equations with Boundary Conditions in Banach Spaces

Abstract

We present the existence of solutions for sequential Caputo–Hadamard fractional differential equations (SC-HFDE) with fractional boundary conditions (FBCs). Known fixed-point techniques are used to analyze the existence of the problem. In particular, the contraction mapping principle is used to investigate the uniqueness results. Existence results are obtained via Krasnoselkii’s theorem. An example is used to illustrate the results. In this way, our work generalizes several recent interesting results.

Keywords

• fractional differential equations
• Caputo–Hadamard fractional derivative
• fractional boundary conditions
• existence and uniqueness