Stability analysis for boundary value problems with generalized nonlocal condition via Hilfer–Katugampola fractional derivative
Idris Ahmed, Poom Kumam, Fahd Jarad, Piyachat Borisut, Kanokwan Sıtthıthakerngkıet, Alhassan Ibrahim
Abstract
Abstract In this research, we present the stability analysis of a fractional differential equation of a generalized Liouville–Caputo-type (Katugampola) via the Hilfer fractional derivative with a nonlocal integral boundary condition. Besides, we derive the relation between the proposed problem and the Volterra integral equation. Using the concepts of Banach and Krasnoselskii’s fixed point theorems, we investigate the existence and uniqueness of solutions to the proposed problem. Finally, we present two examples to clarify the abstract result.
Topics & Concepts
MathematicsUniquenessBoundary value problemFractional calculusMathematical analysisOrdinary differential equationPartial differential equationStability (learning theory)Fixed-point theoremDerivative (finance)Banach spaceIntegral equationVolterra integral equationApplied mathematicsDifferential equationMachine learningFinancial economicsEconomicsComputer scienceFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Boundary Problems