Boundary value problem for nonlinear fractional differential equations of variable order via Kuratowski MNC technique

Abstract

Abstract In the present research study, for a given multiterm boundary value problem (BVP) involving the Riemann-Liouville fractional differential equation of variable order, the existence properties are analyzed. To achieve this aim, we firstly investigate some specifications of this kind of variable-order operators, and then we derive the required criteria to confirm the existence of solution and study the stability of the obtained solution in the sense of Ulam-Hyers-Rassias (UHR). All results in this study are established with the help of the Darbo’s fixed point theorem (DFPT) combined with Kuratowski measure of noncompactness (KMNC). We construct an example to illustrate the validity of our observed results.

Keywords

• Fractional differential equations of variable order
• Boundary value problem
• Darbo’s fixed point theorem
• Measure of noncompactness
• Ulam–Hyers–Rassias stability