In this paper, an extension of Differential transformation method (DTM) which is an analytical-numerical method for solving the fuzzy partial Differential equation (FPDE) by using the strongly generalized differentiability concept is investigated. The proposed algorithm is illustrated by numerical example.

In this paper, a free vibration of nano-plates is investigated considering the small scale parameter. The used rectangular nano-plate is thin and under different boundary conditions. In order to obtain the natural frequencies of the nano-plates, classical plate theory on the basis of non-local theory is used. The governing equation is solved using a semi-analytical method DTM (Differential transformation method). The results for free vibration of those plates are compared with the theoretical data published in the literature. Results show that DTM is a powerful, simple, accurate and fast method for solving equations in comparison with other methods. Non-local parameter is very effective in vibration of nano-plates and its influence is different in various boundary conditions. Influence of this parameter in simply supported-clamp boundary condition is higher than other boundary conditions.

In this paper, the dierential transformation method (DTM) is applied to solve fuzzy fractional heat equations. The elementary properties of this method are given. The approximate and exact solutions of these equations are calculated in the form of series with easily computable terms. The proposed method is also illustrated by some examples. The results reveal that DTM is a highly eective scheme for obtaining approximate analytical solutions of fuzzy fractional heat equations.

This paper presents a novel investigation into the free vibration of porous folded plates using the Differential transformation method (DTM). The porosity is functionally graded (FG) along the thickness of the plate, resulting in material properties that vary with the z-coordinate. The motion equations for each plate segment are derived based on classical plate theory (CPT), with simply-supported boundary conditions applied at the front edges, allowing the transformation of partial Differential equations into ordinary Differential equations. The Differential transformation method is then employed to discretize the motion equations in the x-direction. By applying boundary conditions at the remaining edges and ensuring continuity at the joints, the eigenvalue problem is formulated, leading to the calculation of natural frequencies and mode shapes of the folded plate. The mathematical model is validated through comparisons with finite element method (FEM) results and existing literature. Results indicate that Type C porosity distributions exhibit the highest stiffness and resonant frequency compared to other porosity types. While frequency behavior is consistent across mode numbers regardless of porosity distribution and plate length, the impact of the porosity parameter on the frequency of Type C plates is demonstrably less significant than on other porosity types.