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 solutions first studied using a Darbo’s fixed-point theorem and the Kuratowski measure noncompactness. Secondly, Ulam–Hyers stability criteria are examined. All results in this study established with help generalized intervals piecewise constant functions. We convert Riemann–Liouville variable-order problem equivalent standard fractional-constant orders. Finally, two examples constructed illustrate validity observed results.