Applications of Fixed Point Theory to Investigate a System of Fractional Order Differential Equations
Zareen A. Khan, Israr Ahmad, Kamal Shah
Abstract
We investigate a nonlinear system of pantograph-type fractional differential equations (FDEs) via Caputo-Hadamard derivative (CHD). We establish the conditions for existence theory and Ulam-Hyers-type stability for the underlying boundary value system (BVS) of FDE. We use Krasnoselskii’s and Banach’s fixed point theorems to obtain the desired results for the existence of solution. Stability is an important aspect from a numerical point of view we investigate here. To justify the main work, relevant examples are provided.
Topics & Concepts
Fixed-point theoremMathematicsHadamard transformFixed pointStability (learning theory)Fractional calculusNonlinear systemMathematical analysisApplied mathematicsType (biology)Order (exchange)Differential equationBoundary value problemComputer scienceQuantum mechanicsPhysicsEconomicsMachine learningBiologyFinanceEcologyFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Numerical Methods