Existence and uniqueness results for sequential ψ-Hilfer fractional pantograph differential equations with mixed nonlocal boundary conditions

Abstract

In this paper, we discuss the existence and uniqueness of boundary value problems for sequential ψ-Hilfer fractional pantograph differential equations with mixed nonlocal boundary conditions. The existence results are obtained via the well known Krasnoselskii's fixed point theorem while the uniqueness is demonstrated by using the Banach's contraction mapping principle. Some examples are also given to demonstrate the application of the main results.

Keywords

• existence
• uniqueness
• ψ-hilfer fractional derivative
• pantograph equations
• fixed point theory