Laplace transform formula on fuzzy nth-order derivative and its application in fuzzy ordinary differential equations

Numerical methods for solving fuzzy equations: A survey

“…In [15] the Euler method is used to obtain the approximate solution of the fuzzy initial value problem. In [16] the Laplace transform method is used to obtain the solutions of second-order FDE. In [17] the compound ( G ′ G )-expansion method is proposed to construct the multiple non-traveling wave solutions of nonlinear PDEs.…”

A Proposed Analytical Method for Solving Fuzzy Linear Initial Value Problems

“…In addition, an existence theorem was given for fuzzy-valued function which possesses the fuzzy Laplace transform (5). A formula of the fuzzy Laplace transform of the nthorder derivative was initially introduced in terms of the number of derivatives in form (ii) by Mohammad Ali ( 6), and Haydar and Mohammad Ali (7), it was followed by introducing another formula for the fuzzy Laplace transform on fuzzy nth-order derivative by concept of the strongly generalized differentiability (8). In the direction of solving n-th order FDEs numerically, many efforts have been introduced by a number of authors (9)(10)(11).…”

Fuzzy Differential Equations for Modeling and Control of Fuzzy Systems

“…Some numerical approaches, such as Nystrom method [11] and Runge-Kutta method [12] can also be implemented for resolving FDEs. Laplace transform has been utilized for second-order FDE in [13]. The results of feedback control in refer to the wave equation has been illustrated in [14], whereas the open loop control in concerned to the wave equation has been demonstrated in [15].…”