Numerical solution of systems of second-order boundary value problems using continuous genetic algorithm

In this article, we propose the reproducing kernel Hilbert space method to obtain the exact and the numerical solutions of fuzzy Fredholm---Volterra integrodifferential equations. The solution meth...

Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations

Modeling of uncertainty differential equations is very important issue in applied sciences and engineering, while the natural way to model such dynamical systems is to use fuzzy differential equations. In this paper, we present a new method for solving fuzzy differential equations based on the reproducing kernel theory under strongly generalized differentiability. The analytic and approximate solutions are given with series form in terms of their parametric form in the space $$W_2^2 [a,b]\oplus W_2^2 [a,b].$$W22[a,b]źW22[a,b]. The method used in this paper has several advantages; first, it is of global nature in terms of the solutions obtained as well as its ability to solve other mathematical, physical, and engineering problems; second, it is accurate, needs less effort to achieve the results, and is developed especially for the nonlinear cases; third, in the proposed method, it is possible to pick any point in the interval of integration and as well the approximate solutions and their derivatives will be applicable; fourth, the method does not require discretization of the variables, and it is not effected by computation round off errors and one is not faced with necessity of large computer memory and time. Results presented in this paper show potentiality, generality, and superiority of our method as compared with other well-known methods.

Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method

Solving fuzzy fractional differential equations by fuzzy laplace transforms

In this paper, we investigate the analytic and approximate solutions of second-order, two-point fuzzy boundary value problems based on the reproducing kernel theory under the assumption of strongly generalized differentiability. The solution methodology is based on generating the orthogonal basis from the obtained kernel functions, while the orthonormal basis is constructing in order to formulate and utilize the solutions with series form in terms of their r-cut representation in the space $$\oplus _{j=1}^2 W_2^3 \left[ {a,b}\right] $$źj=12W23a,b. An efficient computational algorithm is provided to guarantee the procedure and to confirm the performance of the proposed method. Results of numerical experiments are provided to illustrate the theoretical statements in order to show potentiality, generality, and superiority of our algorithm for solving such fuzzy equations. Graphical results, tabulated data, and numerical comparisons are presented and discussed quantitatively to illustrate the possible fuzzy solutions.

Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems

In this paper, we interpret a two-point boundary value problem for a second order fuzzy differential equation by using a generalized differentiability concept. We present a new concept of solutions and, utilizing the generalized differentiability, we investigate the problem of finding new solutions. Some examples are provided for which the new solutions are found.

A boundary value problem for second order fuzzy differential equations

Variation of constant formula for first order fuzzy differential equations

Numerical solution of fuzzy differential equations under generalized differentiability

A new fuzzy approximation method to Cauchy problems by fuzzy transform

We firstly present a generalized concept of higher-order differentiability for fuzzy functions. Then we interpret th-order fuzzy differential equations using this concept. We introduce new definitions of solution to fuzzy differential equations. Some examples are provided for which both the new solutions and the former ones to the fuzzy initial value problems are presented and compared. We present an example of a linear second-order fuzzy differential equation with initial conditions having four different solutions.

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Alireza Khastan

Papers

A boundary value problem for second order fuzzy differential equations

Variation of constant formula for first order fuzzy differential equations

Numerical solution of fuzzy differential equations under generalized differentiability

A new fuzzy approximation method to Cauchy problems by fuzzy transform

New Results on Multiple Solutions for th-Order Fuzzy Differential Equations under Generalized Differentiability