Qualitative Properties of Positive Solutions of a Kind for Fractional Pantograph Problems using Technique Fixed Point Theory
Hamid Boulares, Abbes Benchaabane, Nuttapol Pakkaranang, Ramsha Shafqat, Bancha Panyanak
Abstract
The current paper intends to report the existence and uniqueness of positive solutions for nonlinear pantograph Caputo–Hadamard fractional differential equations. As part of a procedure, we transform the specified pantograph fractional differential equation into an equivalent integral equation. We show that this equation has a positive solution by utilising the Schauder fixed point theorem (SFPT) and the upper and lower solutions method. Another method for proving the existence of a singular positive solution is the Banach fixed point theorem (BFPT). Finally, we provide an example that illustrates and explains our conclusions.
Topics & Concepts
Fixed-point theoremMathematicsUniquenessSchauder fixed point theoremPantographBanach fixed-point theoremMathematical analysisHadamard transformPicard–Lindelöf theoremFixed pointNonlinear systemFractional calculusIntegral equationDifferential equationApplied mathematicsPhysicsMechanical engineeringEngineeringQuantum mechanicsNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsContact Mechanics and Variational Inequalities