Semi-analytical solutions of the 3rd order fuzzy dispersive partial differential equations under fractional operators

Abstract

The purpose of this article is to extend the fractional third order dispersive PDE under singular and non-singular fractional operators via the notion of fuzziness. We investigate the fuzzy dispersive PDE in one and higher dimension under Caputo, Caputo-Fabrizio, and Atangana-Baleanu fractional operators and provide two examples to each derivative. We derive the general algorithm and numerical results in series of the models and test problems with the help of fuzzy Laplace transform. The numerical results confirm that solutions obtained in the fuzzy sense are more generalized than the fractional-order solution. We mention in remarks following each example that we recover the solutions of the fractional-order equations by putting the lower and upper functions of the fuzzy number g̃ equals to 1 in the fuzzy solutions of the proposed dispersive PDEs. We demonstrate the numerical results through 2D and 3D plots for different fractional-order and uncertainty k∈[0,1]. We provide a comparison between Caputo, Caputo-Fabrizio and Atangana-Baleanu fuzzy fractional dispersive PDE. In the end, we give the conclusion of the article and future work.

Keywords

• Uncertainty
• Fuzzy dispersive PDE
• Fuzzy Laplace transform