Fuzzy fractional generalized Bagley–Torvik equation with fuzzy Caputo gH-differentiability.

The fractional generalized Bagley–Torvik equation (FGB-TE) is a mathematical description of the motion of an immersed plate in a Newtonian fluid. The analytical study of the FGB-TE with uncertain initial conditions and two independent fractional orders is usually complex and difficult. Therefore, it is necessary to develop a proper and effective technique to solve the fuzzy fractional generalized Bagley–Torvik equation (FFGB-TE) analytically. This paper presents the analytical fuzzy solution of the FFGB-TEs based on the concept of the fuzzy Caputo generalized Hukuhara differentiability (g H -differentiability) using the fuzzy Laplace transform (FLT) technique. The closed-form solution of FFGB-TEs is presented for both the homogeneous and non-homogeneous cases in terms of the Mittag-Leffler function (MLF) involving double series. Several significant results are introduced and proven with true reasoning. We illustrate our proposed analytical approach with the help of several demonstrative examples. To enhance the novelty of the proposed work, we solved the FFGB-TE as an application of the motion of an immersed plate and visualized their graphs to support the theoretical results. • Analytical solutions of fuzzy fractional Bagley-Torvik equation are investigated. • The potential solutions are extracted using fuzzy Caputo g H -differentiability. • Closed-form solutions of proposed scheme are presented using Mittag-Leffler function. • Several significant results are presented using the proposed analytical approach. • The real-world problem is solved as an application of the proposed study. [ABSTRACT FROM AUTHOR]