Adomian decomposition method

Physics

Nonlinear system

Volterra integral equation

Uniqueness

Volterra equations

Mathematics

Economic growth

Biology

Laplace transform

Statistics

Decomposition

Mathematical analysis

Economics

Power (physics)

Integral equation

Ecology

Convergence (economics)

Decomposition method (queueing theory)

Quantum mechanics

Differential equation

Applied mathematics

Reliability (semiconductor)

Fredholm integral equation

Problemy analiza

This paper demonstrates a study on some significant latest innovations in the approximation techniques to find the approximate solutions of Caputo fractional Volterra -Fredholm integro-differential equations.To apply this, the study uses Adomian decomposition method and modified Laplace Adomian decomposition method.A wider applicability of these techniques is based on their reliability and reduction in the size of the computational work.This study provides analytical approximate to determine the behavior of the solution.It proves the existence and uniqueness results and convergence of the solution.In addition, it brings an example to examine the validity and applicability of the proposed techniques.

The Approximate Solutions of Fractional Volterra-Fredholm Integro-Differential Equations by using Analytical Techniques