On a coupled system of pantograph problem with three sequential fractional derivatives by using positive contraction-type inequalities
Reny George, Mohamed Houas, Mehran Ghaderi, Shahram Rezapour, S.K. Elagan
Abstract
This paper aims to establish conditions for the existence, uniqueness and Ulam–Hyers stability of solutions for a coupled system of pantograph problem with three sequential fractional derivatives. Two results on the uniqueness and existence of solutions are proved to utilize the Leray–Schauder and Banach fixed point theorems and positive contraction-type inequalities. Also, the stability in the sense of Ulam–Hyers and Ulam–Hyers–Rassias are studied. An illustrative example with graphical and numerical simulations is also proposed.
Topics & Concepts
UniquenessMathematicsPantographContraction (grammar)Fixed-point theoremContraction mappingFixed pointContraction principleType (biology)Banach spaceStability (learning theory)Mathematical analysisApplied mathematicsPure mathematicsComputer scienceInternal medicineEngineeringBiologyMedicineMechanical engineeringEcologyMachine learningNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsContact Mechanics and Variational Inequalities