Series Type Solution of Fuzzy Fractional Order Swift–Hohenberg Equation by Fuzzy Hybrid Sumudu Transform
Open Access
- 11 May 2022
- journal article
- research article
- Published by Hindawi Limited in Mathematical Problems in Engineering
- Vol. 2022, 1-15
- https://doi.org/10.1155/2022/3864053
Abstract
There are some confusion and complexity in our everyday lives, as we live in an uncertain environment. In such type of environment, an accurate calculation of the data and finding a solution to a problem is not an easy job. So, fuzzy differential equations are the better tools to model problems in the fuzzy domain. Modeling the real-world phenomenon more accurately requires such operators. Therefore, we investigate the fractional-order SwiftHohenberg equation in the fuzzy concept. We study this equation under the fuzzy Caputo fractional derivative. We use the fuzzy Sumudu transform to find out the semianalytical solution of the considered equation. To deal with the nonlinear term of the problem, we also use the Adomian decomposition method. To confirm the accuracy of the proposed procedure, we give two test problems. Lastly, we plot the numerical results for various fractional orders, and uncertainty belongs to [0, 1].This publication has 30 references indexed in Scilit:
- Generalized differentiability of fuzzy-valued functionsFuzzy Sets and Systems, 2013
- On the concept of solution for fractional differential equations with uncertaintyNonlinear Analysis, 2010
- Large time behaviour of solutions of the Swift–Hohenberg equationComptes Rendus Mathematique, 2003
- Swift-Hohenberg Equation for LasersPhysical Review Letters, 1994
- Effects of additive noise at the onset of Rayleigh-Bénard convectionPhysical Review A, 1992
- On the fuzzy initial value problemFuzzy Sets and Systems, 1987
- Fuzzy differential equationsFuzzy Sets and Systems, 1987
- Towards fuzzy differential calculus part 1: Integration of fuzzy mappingsFuzzy Sets and Systems, 1982
- Hydrodynamic fluctuations at the convective instabilityPhysical Review A, 1977
- Fuzzy setsInformation and Control, 1965