The generalized U–H and U–H stability and existence analysis of a coupled hybrid system of integro-differential IVPs involving φ-Caputo fractional operators
Abdelatif Boutiara, Sina Etemad, Azhar Hussain, Shahram Rezapour
Abstract
Abstract We investigate the existence and uniqueness of solutions to a coupled system of the hybrid fractional integro-differential equations involving φ -Caputo fractional operators. To achieve this goal, we make use of a hybrid fixed point theorem for a sum of three operators due to Dhage and also the uniqueness result is obtained by making use of the Banach contraction principle. Moreover, we explore the Ulam–Hyers stability and its generalized version for the given coupled hybrid system. An example is presented to guarantee the validity of our existence results.
Topics & Concepts
MathematicsUniquenessContraction principleOrdinary differential equationContraction mappingFixed-point theoremStability (learning theory)Banach spaceContraction (grammar)Applied mathematicsPartial differential equationDifferential equationMathematical analysisPure mathematicsComputer scienceMedicineInternal medicineMachine learningNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsFixed Point Theorems Analysis