In the beginning, we describe the Fuzzy inner product space and the Fuzzy Hilbert space. Our goal is to use the Fuzzy reproducing kernel method to solve the second-order Fuzzy boundary value problem. The Fuzzy convergence analysis of introduced method is discussed in detail. We present some examples in the end.

The aim of this paper is to use the reproducing kernel Hilbert Space method (RKHSM) to solve the linear and nonlinear Fuzzy impulsive fractional differential equations. Finding the numerical solutions of this class of equations are a difficult topic to analyze. In this study, convergence analysis, estimations error and bounds errors are discussed in detail under some hypotheses which provide the theoretical basis of the proposed algorithm. Some numerical examples indicate that this method is an efficient one to solve the mentioned equations.

In this study, a new approach based on the reproducing kernel Hilbert Space method is proposed to approximate the solution of the second kind Fuzzy linear integral equations. For this purpose, at first by applying the concept of parametric form, the Fuzzy integral equation is converted to a system of crisp integral equations. Then, this system is solved by using the reproducing kernel method free of the Gram-Schmidt orthogonalization process. Also, two numerical algorithms are proposed based on applying the Gram-Schmidt process and without using it. The general form of numerical solution accordingly the reproducing kernel method is introduced and the convergence theorem of solution of the proposed scheme to the exact solution is proved. Finally, a sample Fuzzy integral equation is solved by means of both suggested algorithms and the results are compared for differents points and levels. Due to the difficulties in applying the Gram-Schmidt process, the obtained results of the new algorithm are satisfactory.

Purpose: In this paper, we shall present an algorithm for solving more general singular second-order multi-point boundary value problems.methods: The algorithm is based on the quasilinearization technique and the reproducing kernel method for linear multi-point boundary value problems.Results: Three numerical examples are given to demonstrate the efficiency of the present method.Conclusions: Obtained results show that the present method is quite efficient.

Purpose: In this paper, a new algorithm is presented for solving one-dimensional parabolic partial differential equations subject to integral conditions.methods: The algorithm is based on the transverse method of lines and the reproducing kernel method. The transverse method of lines can reduce a one-dimensional parabolic partial differential equation subject to integral conditions to a series of ordinary differential equations (ODEs) with integral boundary conditions. The reproducing kernel method is a relative new analytical technique, which can solve successfully ODEs with integral boundary conditions.Results: The present method combines advantages of these two methods.Conclusions: Numerical results show that the present method is quite efficient.