A comprehensive view of the solvability of non-local fractional orders pantograph equation with a fractal-fractional feedback control

المجلة: AIMS Mathematics

سنة النشر: 2024

تاريخ النشر: 2024-01-07

In this article, the solvability of the pantograph equation of fractional orders under a fractal-fractional feedback control was investigated. This investigation was located in the class of all continuous functions. The necessary conditions for the solvability of that problem and the continuous dependence of the solution on some parameters and the control variable were established with the help of some fixed point theorems. Additionally, the Hyers-Ulam stability of the issue was explored. Finally, some specific problems extended to the corresponding problem with integer orders were illustrated. The theoretical results were supported by numerical simulations and comparisons with existing results in the literature.

On the existence and Ulam-Hyers stability for implicit fractional differential equation via fractional integral-type boundary conditions

المجلة: Demonstratio Mathematica

سنة النشر: 2024

تاريخ النشر: 2024-01-04

This study investigates the existence of solutions for implicit fractional differential equations with fractional-order integral boundary conditions. We create the required conditions to ensure unique solution and Ulam-Hyers-Rassias stability. We also give examples to highlight the major findings.

ON A COUPLED HYBRID SYSTEM OF ORDINARY SECOND-ORDER NONLINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS

المجلة: TWMS Journal of Applied and Engineering Mathematics

سنة النشر: 2024

تاريخ النشر: 2024-01-05

In this work, the existence of solutions for coupled systems of ordinary second-order hybrid functional differential equations (CSHDE) is considered, due to Dhage's hybrid fixed point theorem. Continuous dependence of the solution of our problem will be proven on delay functions. To demonstrate the produced outcome, an example is provided.