In this paper we propose a method for computing approximations of solution of fuzzy fractional differential equations using fuzzy variational iteration method. Defining a fuzzy fractional derivative, we verify the utility of the method through two illustrative examples.

In this paper, a class of semi-implicit two-stage stochastic Runge-Kuttamethods (SRKs) of strong global order one, with minimum principal er-ror constants are given. These methods are applied to solve It^o stochas-tic di erential equations (SDEs) with a Wiener process. The e ciency ofthis method with respect to explicit two-stage It^o Runge-Kutta methods(IRKs), It^o method, Milstien method, semi-implicit and implicit two-stageStratonovich Runge-Kutta methods are demonstrated by presenting somenumerical results.

By adding a suitable real function on both sides of the quadratic Riccati differential equation, we propose a weighted type of Adams-Bashforth rules for solving it, in which moments are used instead of the constant coefficients of Adams-Bashforth rules. Numerical results reveal that the proposed method is efficient and can be applied for other nonlinear problems.

In this paper, a new type of equation namely fuzzy fractional stochastic Pantograph delay differential system (FSPDDS) is proposed. In our previous work, a first extension of fuzzy stochastic differential system into fuzzy fractional stochastic differential system by using Granular differentiability has been established. Here we study the existence and uniqueness results for the fuzzy FSPDDS which are obtained by using generalized Granular differentiability and contraction principle with weaker conditions. This kind of equation is used in many real world problems. Finally, we provide two numerical examples for the effectiveness of the theoretical results.

Stochastic linear combinations of some random vectors are studied where the dis-tribution of the random vectors and the joint distribution of their coe, cients have Dirichlet distributions. A method is provided for calculating the distribution of these combinations which has been studied before. Our main result is the same as but from a di, erent point of view.

Many quick-link optimization models of transferring corrosive materials, need some constraints to change the output space such that all of the criteria are met, which forms a nonlinear problem with speci, c constraints. So we use an approach for , nding global solutions of mixed-integer nonlinear optimization problems with ordinary di, erential equation constraints on the shortest path problem connective body composition because we need to save time. For the solution of constrained di, erential equations, we present a numerical method by coupling an implicit numerical method, and the results will be expressed by showing that the optimal path is selected.

In this paper, we will investigate existence, comparison and some stability results of set solutions of fuzzy intergo-differential systems under the formDHx (t)=f(t, x (t))+∫tt0 g (t, h, x (h)) dh, x (t0) =x0ÎEnNwith some suitable conditions.

We consider a , rst-order partial di, erential equation with constant irreversible co-e, cients in a Banach space in the regular case. The equation is split into equations in subspaces, in which non-degenerate subsystems are obtained. We obtain an ana-lytical solution of each system with Showalter-type conditions. Finally, an example is given to illustrate the theoretical results.

In this paper, we propose a new numerical algorithm for the approximate solution of non-homogeneous fractional di, erential equation. Using this algorithm the fractional di, erential equations are transformed into a system of algebraic linear equations by operational matrices of block-pulse and hybrid functions. Based on our new algorithm, this system of algebraic linear equations can be solved by a proposed (TSI) method. Further, some numerical examples are given to illustrate and establish the accuracy and reliability of the proposed algorithm.