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In the present paper, we employ the first variation method to derive the fuzzy necessary condition, as a Euler-Lagrange equation for extremizing both the simplest and the generalized fuzzy variational problems. The latter class of problems includes those with higher derivatives, subject to the generalized Hukuhara differentiability. To illustrate the validity of the newly obtained Euler-Lagrange equation, two examples are considered in which the first example is considered with trapezoidal fuzzy numbers as the endpoints conditions while the second example is considered with triangular fuzzy numbers. [ABSTRACT FROM AUTHOR]

The variational iteration approach is introduced in this article to solve linear and nonlinear fractional order random ordinary differential equations., in which it is possible sometimes, especially for linear problems to find the exact solution in a few iterations using this method or finding the approximate solution of the problem, which is most cases very accurate. This technique provides of evaluating a sequence of functions, which is proved to be converge to the exact solution of the problem under consideration. The variational iteration method is a powerful method used to solve a large class of linear and nonlinear problems involving also fractional order random ordinary differential equations, more easily and accurately, and thus it has been widely used in engineering and physical problems. [ABSTRACT FROM AUTHOR]

In this paper, the homotopy perturbation method will be applied to find the approximate solution of fractional order random ordinary differential equations, in which the fractional order derivatives and integrals are defined using Caputo and Riemann-Liouville definitions of fractional derivatives and integrals, respectively. Also, the convergence of the approximated solution is stated and proved in this work. The work is verified for three different examples, which are simulated for different generations of Brownian motion. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to introduce interval two-points fuzzy boundary value problems, in which the fuzziness course when the coefficients of the governing ordinary differential equation and/or the boundary conditions includes fuzzy numbers of either triangular or trapezoidal types. Such equations will be solved by introducing the concept of α – level sets, α ∈ [0,1] to treat the fuzzy ordinary differential equation into two nonfuzzy ordinary differential equations, which are corresponds to the lower and upper solutions of the interval fuzzy solution. The shooting method is applied to solve the resultant equations in both cases, linear and nonlinear. [ABSTRACT FROM AUTHOR]

In this paper, the homotopy analysis method have been utilized for solving non-linear delay differential equations of multi-term fractional order, and the fractional derivative is expressed in the Caputo sense. In this approach, the solutions are found in the form of convergent power series components are easily computed. Some illustrative examples are simulated using computer programs written in Mathcad 15 computer software and then a comparison between the exact solution and the approximate results are presented to show the reliability and the accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, we shall introduce the homtopy perturbation method which was applied to obtain the approximate solution of the fractional order random integro-differential equations.The proof of the convergence of the obtained sequence of approximate solutions to the exact solution also introduced and presented. In addition, it may be noted that it is not easy to obtain the approximate solution using the homotopy perturbation method because of the existence of the Brownian motion or Winner process. Moreover, numerical results shows that our theoretical analysis are accurate and the homtopy perturbation method can be considered as a powerful method for solving fractional order random integro-differential equations. [ABSTRACT FROM AUTHOR]

In this work, a result (which stated for parameter invariant 1-dimensional systems) is extended to LPV multidimensional systems via applying the hyperdiagonal operators instead of standard matrices, where these operators help in applying the methods to LPV systems. A comparison between the standard controller design problem and the ex-tended controller design for parameter varying multidimensional system has been stated, where an improved (minimized) induced-norm of the system has been computed by following the result of this paper. The improvement of the result is done by relaxing the condition to be solved via adding an extra slack variable which gives more degree of freedom in solving the condition. The validation of our results is illustrated with a 2-dimensional parameter-varying system example. [ABSTRACT FROM AUTHOR]

In this paper, we will introduce an approximate solution of nonhomogeneous Riccati matrix differential equations with time delay using one of He's iterative methods, namely, variational iteration method. The solution of the considered model of the Riccati differential equation are evaluated in the form of a convergent series with iterated components and also derive the sequence of variational iteration formula and prove it convergent. In addition, illustrative examples are considered and solved in connection with the method of steps for solving delay differential equation. [ABSTRACT FROM AUTHOR]