The Residual Power Series Method for Solving the Fractional Fuzzy Delay Differential Equation
In this paper, the fuzzy delay differential equation is expressed in fractional form, and the Residual Power Series Method (RPSM) is used to solve the equation. The delay differential equation indicates that in a system, the speed of the system is not only related to the current state of the system, but also depends on the historical trajectory until this moment. Due to the existence of systematic errors, fractional fuzzy delay differential equations play an important role in more and more system models in biology, engineering, physics and other sciences. Maple was used to calculate the numerical solution of this equation, and the results are presented in the form of a graph. The results show that it is an effective method when solving the fractional fuzzy delay differential equation. By this method, the approximate solutions of the fractional fuzzy delay differential equation can be obtained with just a few steps.
KeywordsResidual Power Series Method Fractional fuzzy delay differential equation Caputo derivative
- 2.Jafari, R.: Solving fuzzy differential equation with bernstein neural networks. In: 2016 IEEE International Conference on Systems, Man, and Cybernetics \(\bullet \) SMC 2016, pp. 001245-001250. IEEE, Budapest (2016)Google Scholar
- 4.Ahmad, L., Farooq, M., Abdullah, S.: Solving n-th order fuzzy differential equation by fuzzy Laplace transform. Indian J. Pure Appl. Math. (2014) Google Scholar
- 14.Podlubny, I.: Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. In: Mathematics in Science and Engineering , vol. 198, pp. 1–340 (1999)Google Scholar
- 16.Hamood, M.Y., Ali, F.J.: New analytical method for solving fuzzy delay differential equations. In: AIP Conference Proceedings, vol. 1691, pp. 040028-1–040028-8. AIP Publishing, Malaysia (2015)Google Scholar