Boundary-Value Problem for Nonlinear Fractional Differential Equations of Variable Order with Finite Delay via Kuratowski Measure of Noncompactness
Benoumran Telli, Mohammed Said Souıd, Ivanka Stamova
Abstract
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.
Topics & Concepts
MathematicsMathematical analysisMeasure (data warehouse)Constant (computer programming)Nonlinear systemOrder (exchange)Boundary value problemVariable (mathematics)Fixed-point theoremPiecewiseFractional calculusDifferential equationApplied mathematicsPhysicsDatabaseProgramming languageFinanceEconomicsComputer scienceQuantum mechanicsFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisNumerical methods for differential equations