Approximate solution for a fractional BVP under Ψ‐Riemann–Liouville operators via iterative method and artificial neural networks
Authors:
- 22 March 2023
- journal article
- research article
- Published by Wiley in Mathematical Methods in the Applied Sciences
- Vol. 46 (12) , 12826-12839
Abstract
In this work, we discussed the existence and uniqueness of the solution for a fractional boundary value problem involving the ‐Riemann–Liouville operators where we used Banach's fixed point theorem; after that, we applied an iterative method and artificial neural networks technique to solve our main problem. Finally, the approximate solution was plotted.Keywords
This publication has 16 references indexed in Scilit:
- An efficient method for nonlinear fractional differential equations: combination of the Adomian decomposition method and spectral methodIndian Journal of Pure and Applied Mathematics, 2014
- Numerical solutions of the initial value problem for fractional differential equations by modification of the Adomian decomposition methodFractional Calculus and Applied Analysis, 2014
- An iterative method for solving nonlinear functional equationsJournal of Mathematical Analysis and Applications, 2006
- Adomian decomposition: a tool for solving a system of fractional differential equationsJournal of Mathematical Analysis and Applications, 2005
- Solution of a system of Volterra integral equations of the first kind by Adomian methodApplied Mathematics and Computation, 2003
- The modified decomposition method for solving nonlinear algebraic equationsApplied Mathematics and Computation, 2002
- Approximation capabilities of multilayer feedforward networksNeural Networks, 1991
- Approximation by superpositions of a sigmoidal functionMathematics of Control, Signals, and Systems, 1989
- The perceptron: A probabilistic model for information storage and organization in the brain.Psychological Review, 1958
- A logical calculus of the ideas immanent in nervous activityBulletin of Mathematical Biology, 1943