Some properties of implicit impulsive coupled system via φ-Hilfer fractional operator
Mohammed A. Almalahi, Satish K. Panchal
Abstract
Abstract The major goal of this work is investigating sufficient conditions for the existence and uniqueness of solutions for implicit impulsive coupled system of φ -Hilfer fractional differential equations (FDEs) with instantaneous impulses and terminal conditions. First, we derive equivalent fractional integral equations of the proposed system. Next, by employing some standard fixed point theorems such as Leray–Schauder alternative and Banach, we obtain the existence and uniqueness of solutions. Further, by mathematical analysis technique we investigate the Ulam–Hyers (UH) and generalized UH (GUH) stability of solutions. Finally, we provide a pertinent example to corroborate the results obtained.
Topics & Concepts
MathematicsUniquenessOrdinary differential equationOperator (biology)Stability (learning theory)Applied mathematicsFixed-point theoremPartial differential equationBanach spaceMathematical analysisFixed pointDifferential equationComputer scienceChemistryGeneBiochemistryRepressorMachine learningTranscription factorNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsDifferential Equations and Numerical Methods