Boundary-Value Problem for Nonlinear Fractional Differential Equations of Variable Order with Finite Delay via Kuratowski Measure of Noncompactness

This paper is devoted to boundary-value problems for Riemann-Liouville-type fractional differential equations of variable order involving finite delays. The existence of solutions is first studied using a Darbo's fixed-point theorem and the Kuratowski measure of noncompactness. Secondly, the Ulam-Hyers stability criteria are examined. All of the results in this study are established with the help of generalized intervals and piecewise constant functions. We convert the Riemann-Liouville fractional variable-order problem to equivalent standard Riemann-Liouville problems of fractional-constant orders. Finally, two examples are constructed to illustrate the validity of the observed results.

Automated summary

This paper investigates boundary-value problems for Riemann-Liouville-type fractional differential equations of variable order involving finite delays. The existence of solutions is analyzed using Darbo's fixed-point theorem and the Kuratowski measure of noncompactness. Furthermore, the Ulam-Hyers stability criteria are examined. The results are established using generalized intervals and piecewise constant functions. The conversion of the Riemann-Liouville fractional variable-order problem to equivalent standard Riemann-Liouville problems of fractional-constant orders is also demonstrated. Two examples are provided to illustrate the validity of the obtained results.