In this article, we present the fuzzy Adomian decomposition method (ADM) and fuzzy modified Laplace decomposition method (MLDM) to obtain the solutions of fuzzy fractional Navier–Stokes equations in a tube under fuzzy fractional derivatives. We have looked at the turbulent flow of a viscous fluid in a tube, where the velocity field is a function of only one spatial coordinate, in addition to time being one of the dependent variables. Furthermore, we investigate the fuzzy Elzaki transform, and the fuzzy Elzaki decomposition method (EDM) applied to solving fuzzy linear-nonlinear Schrodinger differential equations. The proposed method worked perfectly without any need for linearization or discretization. Finally, we compared the fuzzy reduced differential transform method (RDTM) and fuzzy homotopy perturbation method (HPM) to solving fuzzy heat-like and wave-like equations with variable coefficients. The RDTM and HPM solutions are simpler than other already existing methods. Several examples are provided to illustrate the methods that have been offered. The results obtained using the scheme presented here agree well with the analytical solutions and the numerical results presented elsewhere. These studies are important in the context of the development of the theory of fuzzy partial differential equations.

In this paper, we present a comparison of several important methods to solve fuzzy partial differential equations (PDEs). These methods include the fuzzy reduced differential transform method (RDTM), fuzzy Adomian decomposition method (ADM), fuzzy Homotopy perturbation method (HPM), and fuzzy Homotopy analysis method (HAM). A distinguishing practical feature of these techniques is administered without the need to use discretion or restricted assumptions. Moreover, we investigate the fuzzy $(n+1)$-dimensional fractional RDTM to obtain the solutions of fuzzy fractional PDEs. The much more distinctive element of this method is that it requires no predetermined assumptions, and reduces the computational effort. We apply the suggested techniques to a set of initial valued problems and get approximate numerical solutions for linear and nonlinear time-fractional PDEs. It is demonstrated that the fuzzy $(n+1)$-dimensional fractional RDTM is both accurate and simple to use. The methods are based on gH-differentiability and fuzzy fractional derivatives. Some illustrative numerical examples are given to demonstrate the effectiveness of our proposed methods. The results show that the methods are powerful mathematical tools for solving fuzzy partial differential equations.

In this article, the authors study the comparison of the generalization differential transform method (DTM) and fuzzy variational iteration method (VIM) applied to determining the approximate analytic solutions of fuzzy fractional KdV, K(2,2) and mKdV equations. Furthermore, we establish the approximation solution two-and three-dimensional fuzzy time-fractional telegraphic equations via the fuzzy reduced differential transform method (RDTM). Finding an exact or closed-approximation solution to a differential equation is possible via fuzzy RDTM. Finally, we present the fuzzy fractional variational homotopy perturbation iteration method (VHPIM) with a modified Riemann-Liouville derivative to solve the fuzzy fractional diffusion equation (FDE). Using this approach achieves a rapidly convergent sequence that approaches the exact solution of the equation. The proposed methods are investigated based on fuzzy fractional derivatives with some illustrative examples. The results reveal that the schemes are highly effective for obtaining the solutions to fuzzy fractional partial differential equations.

In this article, we prove the boundedness of the parametric Marcinkiewicz integral and its higher-order commutators generated by BMO spaces on the variable Morrey-Herz space. All the results are new even when α · is a constant.

This work considers the three-dimensional incompressible rotating magnetohydrodynamics equation spaces with fractional dissipation ${(-\Delta )}^{\wp }$ for $\frac{1}{2}<\wp \le 1$. Furthermore, we use the Littlewood–Paley decomposition and frequency localization techniques to establish the global well-posedness of fractional rotating magnetohydrodynamics equations in a more generalized Besov spaces characterized by the time evolution semigroup related to the generalized linear Stokes–Coriolis operator.

In this article, the authors study the boundedness of the vector-valued inequality for the intrinsic square function and the boundedness of the scalar-valued intrinsic square function on variable exponents Herz spaces ${\dot{K}}_{\rho (·)}^{\alpha ,q(·)}\left({\mathbb{R}}^n\right)$. In addition, the boundedness of commutators generated by the scalar-valued intrinsic square function and BMO class is also studied on ${\dot{K}}_{\rho (·)}^{\alpha ,q(·)}\left({\mathbb{R}}^n\right)$.