a b s t r a c t This paper presents a novel technique for solving two new form of equation with fuzzy and integrodifferential equations. The proposed numerical iterative technique is based on the use of the reproducing Kernel theory. Two numerical examples are given to show the effectiveness and performance of the proposed technique. Simulation results are illustrated and comparative studies with past published works to the exact solution from Laplace transform of order integer have been performed to emphasize the simplicity and accuracy of the proposed technique. Moreover, future applications of the proposed technique are also discussed. Numerical experimental results fully support the findings of the proposed analytical approaches. Ó 2017 The Authors. Production and hosting by Elsevier B.V. on behalf of King Saud University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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This paper reveals a computational method using a Residual Power Series Method (RPSM) for the solution of fuzzy fractional riccati equation under caputo fractional differentiability. An analytical solution of fuzzy fractional riccati equation is obtained as a convergent fractional power series. The procedure produces solutions of high accuracy, and some illustrative examples are solved with a different value of orders to show the efficiency of the RPSM.

In this paper, we use the modified reproducing kernel Hilbert space method to approximate the solution of fuzzy differential equations of fractional order. Using this method, we construct a new algorithm to approximate the solution of such differential equations. The proposed algorithm produces solutions in terms of interval-valued fuzzy numbers. Two numerical examples are tested and the results showed that the proposed algorithm is able to produce solutions that approach to the exact solutions. It concludes that the proposed algorithm can be considered as a modern algorithm that complements to the existing ones. c ○2017 All rights reserved.Keywords: Caputo fractional derivative, fuzzy differential equation of fractional order, modified reproducing kernel Hilbert space method. 2010 MSC: 34A08, 34A07, 47B32.

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