## African Diaspora Journal of Mathematics

- Afr. Diaspora J. Math. (N.S.)
- Volume 15, Number 2 (2013), 87-100.

### Existence and Attractivity Results for Some Fractional Order Partial Integro-differential Equations with Delay

S. Abbas, M. Benchohra, and T. Diagana

#### Abstract

In this paper we study some existence, uniqueness, estimates and global asymptotic stability results for some functional integro-differential equations of fractional order with finite delay. To achieve our goals we make extensive use of some fixed point theorems as well as the so-called Pachpatte techniques.

#### Article information

**Source**

Afr. Diaspora J. Math. (N.S.) Volume 15, Number 2 (2013), 87-100.

**Dates**

First available in Project Euclid: 5 January 2014

**Permanent link to this document**

http://projecteuclid.org/euclid.adjm/1388953704

**Mathematical Reviews number (MathSciNet)**

MR3161669

**Subjects**

Primary: 26A33: Fractional derivatives and integrals 45G05: Singular nonlinear integral equations

**Keywords**

Functional integro-differential equation left-sided mixed Riemann-Liouville integral of fractional order Caputo fractional-order derivative contraction solution estimation finite delay periodic function asymptotic stability fixed point

#### Citation

Abbas, S.; Benchohra, M.; Diagana, T. Existence and Attractivity Results for Some Fractional Order Partial Integro-differential Equations with Delay. African Diaspora Journal of Mathematics. New Series 15 (2013), no. 2, 87--100. http://projecteuclid.org/euclid.adjm/1388953704.