Non‐instantaneous impulsive fractional integro‐differential equations with proportional fractional derivatives with respect to another function
Mohamed I. Abbas
Abstract
This paper concerns the existence and uniqueness of solutions of non‐instantaneous impulsive fractional integro‐differential equations with proportional fractional derivatives with respect to another function. By the aid of the nonlinear alternative of Leray‐Schauder type and the Banach contraction mapping principle, the main results are demonstrated. Two examples are inserted to illustrate the applicability of the theoretical results.
Topics & Concepts
MathematicsUniquenessFractional calculusContraction mappingMathematical analysisNonlinear systemContraction principleFunction (biology)Differential equationContraction (grammar)Type (biology)Fixed-point theoremApplied mathematicsMedicineEvolutionary biologyQuantum mechanicsBiologyEcologyPhysicsInternal medicineFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Numerical Methods