Existence and stability results of pantograph equation with three sequential fractional derivatives
Mohamed Houas, Kirti Kaushik, Anoop Kumar, Aziz Khan, Thabet Abdeljawad
Abstract
<abstract><p>The subject of this work is the existence and Mittag-Leffler-Ulam (MLU) stability of solutions for fractional pantograph equations with three sequential fractional derivatives. Sufficient conditions for the existence and uniqueness of solutions are constructed by utilizing well-known classical fixed point theorems such as the Banach contraction principle, and Leray-Schauder nonlinear alternative. The generalized singular Gronwall's inequality is used to show the MLU stability results. An illustrated example is provided to support the main findings.</p></abstract>
Topics & Concepts
MathematicsUniquenessFixed-point theoremContraction principleFractional calculusStability (learning theory)Contraction (grammar)Nonlinear systemMathematical analysisGronwall's inequalityContraction mappingMathematics Subject ClassificationApplied mathematicsWork (physics)Pure mathematicsInequalityComputer scienceThermodynamicsMedicineQuantum mechanicsInternal medicinePhysicsMachine learningNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsDifferential Equations and Numerical Methods