## Homotopy Analysis Method for Solving a Class of Nonlinear Mixed Volterra-Fredholm Integro-Differential Equations of Fractional Order

**Authors:** Zaid Laadjal

In this paper, we describe the solution approaches based on Homotopy Analysis Method for the follwing Nonlinear Mixed Volterra-Fredholm integro-differential equation of fractional order $$^{C}D^{\alpha }u(t)=\varphi (t)+\lambda \int_{0}^{t}\int_{0}^{T}k(x,s)F\left( u(s\right) )dxds,$$ $$u^{(i)}(0)=c_{i},i=0,...,n-1,$$ where $t\in \Omega =\left[ 0;T\right] ,\ k:\Omega \times \Omega \longrightarrow \mathbb{R},$ $\varphi :\Omega \longrightarrow \mathbb{R},$ are known functions,\ $F:C\left(\Omega, \mathbb{R}\right) \longrightarrow \mathbb{R}$ is nonlinear function, $c_{i} (i=0,...,n-1),$ and $\lambda $ are constants, $^{C}D^{\alpha }$ is the Caputo derivative of order $\alpha $ with $n-1<\alpha \leq n.$ In addition some examples are used to illustrate the accuracy and validity of this approach.

**Comments:** 10 Pages.

**Download:** **PDF**

### Submission history

[v1] 2018-10-24 14:59:24

[v2] 2018-11-17 09:34:46

**Unique-IP document downloads:** 35 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*