## African Diaspora Journal of Mathematics

### Existence Results for Nonlinear Fractional Differential Equations with Four-Point Nonlocal Type Integral Boundary Conditions

#### Abstract

In this paper, we investigate some new existence results for nonlinear fractional differential equations of order $q \in (1,2]$ with four-point nonlocal integral boundary conditions by applying standard fixed point theorems and Leray-Schauder degree theory. Our results are new in the sense that the nonlocal parameters in four-point integral boundary conditions for the problem appear in the integral part of the conditions in contrast to the available literature on four-point fractional boundary value problems which deals with the four-point boundary conditions restrictions on the solution or gradient of the solution of the problem. Some illustrative examples are presented.

#### Article information

Source
Afr. Diaspora J. Math. (N.S.), Volume 11, Number 1 (2011), 29-39.

Dates
First available in Project Euclid: 21 April 2011

Mathematical Reviews number (MathSciNet)
MR2792208

Zentralblatt MATH identifier
1241.26004

Subjects
Primary: 26A33: Fractional derivatives and integrals
Secondary: 34A12 34A40

#### Citation

Ahmad, Bashir; Ntouyas, Sotiris K. Existence Results for Nonlinear Fractional Differential Equations with Four-Point Nonlocal Type Integral Boundary Conditions. Afr. Diaspora J. Math. (N.S.) 11 (2011), no. 1, 29--39. https://projecteuclid.org/euclid.adjm/1303391943