Author:
Mouffak Benchohra ,Abderrahmane Boukenkoul
Abstract
We present an existence and uniqueness theorem for $\mathrm{H}$ - integral equations of fractional order involving fuzzy set valued mappings of a real variable whose values are normal, convex, upper semi continuous and compactly supported fuzzy sets in $\mathbb{R}^n$. The method of successive approximation is the main tool in our analysis.
Subject
Geology,Ocean Engineering,Water Science and Technology
Reference26 articles.
1. S. Abbas, M. Benchohra and G.M. N’Guérékata, Topics in Fractional Differential Equations, Springer, New York, 2012.
2. R.P. Agarwal, M. Benchohra, D. O’Regan and A. Ouahab, Fuzzy solutions for multi-point boundary value problems, Mem. Differential Equations Math. Phys., 35(2005), 1-14.
3. R. P. Agarwal, V. Lakshmikantham and J. J. Nieto, On the concept of solution for fractional differential equations with uncertainty, Nonlinear Anal., 72(2010), 2859-2862.
4. R.P. Agarwal, D. O’Regan, and V. Lakshmikantham, Fuzzy Volterra integral equations: a stacking theorem approach, Appl. Anal., 83(5)(2004), 521-532.
5. A. Arara and M. Benchohra, Fuzzy solutions for boundary value problems with integral boundary conditions, Acta Math. Univ. Comenianae, LXXV(1)(2006), 119-126.