Stability analysis for fractional order implicit <i>ψ</i>‐Hilfer differential equations
Asma Asma, J. F. Gómez‐Aguilar, Ghaus ur Rahman, Maryam Javed
Abstract
The present research endeavor contains formulation of a new ψ ‐Hilfer differential equation equipped with integral‐type subsidiary conditions. Utilizing Picard operator method, Banach contraction principle, and Gronwall inequality, we explore solution's properties of the underlying problem. We provide some assumptions to set up results related to uniqueness of solution for the underlying model. Furthermore, stability analysis is studied in the sense of Ulam Hyers Mittag Leffler's definition. We furnish illustrative examples for the vindication of our obtained analytical results.
Topics & Concepts
MathematicsUniquenessContraction principleStability (learning theory)Gronwall's inequalityApplied mathematicsBanach spaceDifferential equationType (biology)Operator (biology)Order (exchange)Mathematical analysisMathematical economicsInequalityComputer scienceChemistryBiologyRepressorTranscription factorBiochemistryMachine learningFinanceGeneEconomicsEcologyNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsDifferential Equations and Boundary Problems