Boundary problems of sequential fractional differential equations having a monomial coefficient

Abstract

The article examines sequential fractional-order differential equations composed of monomial coefficients defined as nonlinear boundary problems. The original problem is converted into an integral equation in an equivalent form. The contraction mapping principle and Krasnoselskii's fixed-point theorem are implemented to obtain two existence conditions. The problem of Ulam-Hyers stability is also investigated. An illustration is presented to showcase practical application of the obtained results.

Keywords

• Sequential fractional differential equation
• Monomial coefficient
• Boundary value problem
• Existence of solutions
• Stability of Ulam-Hyers