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Random fuzzy fractional integral equations - theoretical foundations

机译：随机模糊分数积分方程-理论基础

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This paper presents mathematical foundations for studies of random fuzzy fractional integral equations which involve a fuzzy integral of fractional order. We consider two different kinds of such equations. Their solutions have different geometrical properties. The equations of the first kind possess solutions with trajectories of nondecreasing diameter of their consecutive values. On the other hand, the solutions to equations of the second kind have trajectories with nonincreasing diameter of their consecutive values. Firstly, the existence and uniqueness of solutions is investigated. This is showed by using a method of successive approximations. An estimation of error of nth approximation is given. Also a boundedness of the solution is indicated. To show well-posedness of the considered theory, we prove that solutions depend continuously on the data of the equations. Some concrete examples of random fuzzy fractional integral equations are solved explicitly. (C) 2014 Elsevier B.V. All rights reserved.
机译：本文为研究包含分数阶模糊积分的随机模糊分数积分方程提供了数学基础。我们考虑两种不同的这类方程。他们的解决方案具有不同的几何特性。第一类方程具有其连续值的直径不减小的轨迹的解。另一方面，第二类方程的解具有其连续值的直径不增加的轨迹。首先，研究了解的存在性和唯一性。通过使用逐次逼近的方法可以证明这一点。给出了第n个近似的误差估计。还指出了解的有界性。为了证明所考虑理论的正确性，我们证明了解决方案连续取决于方程式的数据。明确地解决了随机模糊分数积分方程的一些具体例子。 （C）2014 Elsevier B.V.保留所有权利。

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