Combining fractional differential transform method and reproducing kernel Hilbert space method to solve fuzzy impulsive fractional differential equations

Abstract

The aim of this paper is to use the combination of Reproducing kernel Hilbert space method (RKHSM) and fractional differential transform method (FDTM) 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.

Radu–Miheţ method for UHML stability for a class of ξ‐Hilfer fractional differential equations in matrix valued fuzzy Banach spaces

“…Approximation of functional equations was studied in MVFN spaces, fuzzy metric spaces and random multi‐normed space 7–10 . Also, stability results for stochastic fractional differential and integral equations were considered in previous works 11–18 …”

“…Approximation of functional equations was studied in MVFN spaces, fuzzy metric spaces and random multi-normed space. [7][8][9][10] Also, stability results for stochastic fractional differential and integral equations were considered in previous works. [11][12][13][14][15][16][17][18] Now, we present an alternative fixed point theorem from the literature:…”

Kernel functions‐based approach for distributed order diffusion equations

“…Based on the RKFs theory [10], a class of numerical approaches to solve differential and integral equations were developed and improved (see, e.g., [1–5, 7, 8, 23–27, 30, 33, 34, 36, 39, 40]). In order to solve (2.2) on the basis of the RKFs theory, we shall introduce the approximation in the RKHS and the Mittag‐Leffler RKFs for estimating Caputo time fractional derivative.…”

On the solutions of boundary value problems

“…Safari et al [1] have investigated the rainfallrunoff modeling through regression in the reproducing kernel Hilbert space algorithm. Najafi et al [2] have worked on the combining fractional differential transform method and reproducing kernel Hilbert space method to solve fuzzy impulsive fractional differential equations. Sahihi et al [3] have searched the system of second-order boundary value problems using a new algorithm based on the reproducing kernel Hilbert space.…”