Stability analysis of initial value problem of pantograph-type implicit fractional differential equations with impulsive conditions
Arshad Ali, Ibrahim Mahariq, Kamal Shah, Thabet Abdeljawad, Bahaa Al-Sheikh
Abstract
Abstract In this paper, we study an initial value problem for a class of impulsive implicit-type fractional differential equations (FDEs) with proportional delay terms. Schaefer’s fixed point theorem and Banach’s contraction principle are the key tools in obtaining the required results. We apply our results to a numerical problem for demonstration purpose.
Topics & Concepts
MathematicsContraction principleFixed-point theoremOrdinary differential equationType (biology)Initial value problemMathematical analysisC0-semigroupDifferential equationPantographApplied mathematicsEcologyEngineeringMechanical engineeringBiologyNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsDifferential Equations and Numerical Methods