On Hilfer fractional difference operator
Syed Sabyel Haider, Mujeeb ur Rehman, Thabet Abdeljawad
Abstract
Abstract In this article, a new definition of fractional Hilfer difference operator is introduced. Definition based properties are developed and utilized to construct fixed point operator for fractional order Hilfer difference equations with initial condition. We acquire some conditions for existence, uniqueness, Ulam–Hyers, and Ulam–Hyers–Rassias stability. Modified Gronwall’s inequality is presented for discrete calculus with the delta difference operator.
Topics & Concepts
MathematicsUniquenessOperator (biology)Fractional calculusPartial differential equationOrdinary differential equationApplied mathematicsFixed pointStability (learning theory)Mathematical analysisDifferential equationBiochemistryTranscription factorComputer scienceChemistryMachine learningGeneRepressorNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsFunctional Equations Stability Results