Stability of the mixed Caputo fractional integro-differential equation by means of weighted space method
Open Access
- 1 January 2022
- journal article
- research article
- Published by American Institute of Mathematical Sciences (AIMS) in AIMS Mathematics
- Vol. 7 (2), 2498-2511
- https://doi.org/10.3934/math.2022140
Abstract
In this research work, we consider a class of nonlinear fractional integro-differential equations containing Caputo fractional derivative and integral derivative. We discuss the stabilities of Ulam-Hyers, Ulam-Hyers-Rassias, semi-Ulam-Hyers-Rassias for the nonlinear fractional integro-differential equations in terms of weighted space method and Banach fixed-point theorem. After the demonstration of our results, an example is given to illustrate the results we obtained.Keywords
This publication has 29 references indexed in Scilit:
- Simplified iterative reproducing kernel method for handling time-fractional BVPs with error estimationAin Shams Engineering Journal, 2018
- Ulam Type Stability for a Coupled System of Boundary Value Problems of Nonlinear Fractional Differential EquationsJournal of Function Spaces, 2017
- Blowing-up solutions of multi-order fractional differential equations with the periodic boundary conditionAdvances in Difference Equations, 2017
- Approximate Series Solution of Nonlinear, Fractional Klein-Gordon Equations Using Fractional Reduced Differential Transform MethodJournal of Mathematics and Statistics, 2016
- Numerical approximations for Volterra’s population growth model with fractional order via a multi-domain pseudospectral methodApplied Mathematical Modelling, 2015
- On the rational second kind Chebyshev pseudospectral method for the solution of the Thomas–Fermi equation over an infinite intervalJournal of Computational and Applied Mathematics, 2014
- Fractional Calculus: An Introduction for PhysicistsPhysics Today, 2012
- Fractional cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutionsJournal of Mathematical Biology, 2009
- Numerical solutions of the nonlinear integro-differential equations: Wavelet-Galerkin method and homotopy perturbation methodApplied Mathematics and Computation, 2007
- Solving linear integro-differential equation with Legendre waveletsInternational Journal of Computer Mathematics, 2004