On a general class of nth order sequential hybrid fractional differential equations with boundary conditions

Abstract

This manuscript is related to consider a general class of nth order sequential hybrid fractional differential equations (S-HFDEs) with boundary conditions. With the help of the coincidence degree theory of topology, some appropriate results for the existence theory of the aforementioned class are developed. The mentioned degree theory is a powerful tool to investigate nonlinear problems for qualitative theory. A result related to Ulam-Hyers (U-H) stability is also developed for the considered problem. It should be kept in mind that the considered degree theory relaxes the strong compact condition by some weaker one. Hence, it is used as a sophisticated tool in the investigation of the existence theory of solutions to nonlinear problems. Also, an example is given.

Keywords

• fractional caputo derivative
• sequential hybrid fractional differential equations
• degree theory
• ulam-hyers stability