## International Journal of Differential Equations

- Int. J. Differ. Equ.
- Volume 2017 (2017), Article ID 2097317, 10 pages.

### Collocation Method Based on Genocchi Operational Matrix for Solving Generalized Fractional Pantograph Equations

Abdulnasir Isah, Chang Phang, and Piau Phang

#### Abstract

An effective collocation method based on Genocchi operational matrix for solving generalized fractional pantograph equations with initial and boundary conditions is presented. Using the properties of Genocchi polynomials, we derive a new Genocchi delay operational matrix which we used together with the Genocchi operational matrix of fractional derivative to approach the problems. The error upper bound for the Genocchi operational matrix of fractional derivative is also shown. Collocation method based on these operational matrices is applied to reduce the generalized fractional pantograph equations to a system of algebraic equations. The comparison of the numerical results with some existing methods shows that the present method is an excellent mathematical tool for finding the numerical solutions of generalized fractional pantograph equations.

#### Article information

**Source**

Int. J. Differ. Equ., Volume 2017 (2017), Article ID 2097317, 10 pages.

**Dates**

Received: 2 January 2017

Revised: 16 March 2017

Accepted: 16 May 2017

First available in Project Euclid: 19 July 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.ijde/1500429717

**Digital Object Identifier**

doi:10.1155/2017/2097317

**Mathematical Reviews number (MathSciNet)**

MR3666267

**Zentralblatt MATH identifier**

06915928

#### Citation

Isah, Abdulnasir; Phang, Chang; Phang, Piau. Collocation Method Based on Genocchi Operational Matrix for Solving Generalized Fractional Pantograph Equations. Int. J. Differ. Equ. 2017 (2017), Article ID 2097317, 10 pages. doi:10.1155/2017/2097317. https://projecteuclid.org/euclid.ijde/1500429717