Qualitative Properties of Positive Solutions of a Kind for Fractional Pantograph Problems using Technique Fixed Point Theory
Open Access
- 14 October 2022
- journal article
- research article
- Published by MDPI AG in Fractal and Fractional
- Vol. 6 (10), 593
- https://doi.org/10.3390/fractalfract6100593
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.Keywords
This publication has 27 references indexed in Scilit:
- Fractional equations and generalizations of Schaefer’s and Krasnoselskii’s fixed point theoremsNonlinear Analysis, 2012
- Existence of solutions of initial value problems for nonlinear fractional differential equations on the half-axisNonlinear Analysis, 2011
- Existence of positive solution for singular fractional differential equationApplied Mathematics and Computation, 2009
- Existence of fractional neutral functional differential equationsComputers & Mathematics with Applications, 2009
- Positive solutions of a boundary value problem for a nonlinear fractional differential equationElectronic Journal of Qualitative Theory of Differential Equations, 2008
- Fixed points, Volterra equations, and Becker’s resolventActa Mathematica Hungarica, 2005
- Positive solutions for boundary value problem of nonlinear fractional differential equationJournal of Mathematical Analysis and Applications, 2005
- Existence and Uniqueness for a Nonlinear Fractional Differential EquationJournal of Mathematical Analysis and Applications, 1996
- Stability of the discretized pantograph differential equationMathematics of Computation, 1993
- On a Special Functional EquationJournal of the London Mathematical Society, 1940