Series Type Solution of Fuzzy Fractional Order Swift–Hohenberg Equation by Fuzzy Hybrid Sumudu Transform

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 Swift–Hohenberg 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].