###### Abstract  
In this article, a new analytical technique based on an innovative transformation is used to solve (2+time fractional-order) dimensional physical models. The proposed method is the hybrid methodology of Shehu transformation along with Adomian decomposition method. The series form solution is obtained by using the suggested method which provides the desired rate of convergence. Some numerical examples are solved by using the proposed method. The solutions of the targeted problems are represented by graphs which have confirmed closed contact between the exact and obtained solutions of the problems. Based on the novelty and straightforward implementation of the method, it is considered to be one of the best analytical techniques to solve linear and non-linear fractional partial differential equations. Shehu transformation; Adomian decomposition; analytical solution; Caputo derivatives; (2+time fractional-order) dimensional physical models 2020 10 10.3390/app10010  
fractional design of hepatitis B virus [10], fractional modeling chickenpox disease [11], fractional blood ethanol concentration model [12], fractional model for tuberculosis [13], fractional vibration equation [14], fractional Black-Scholes option pricing equations [15], fractionally damped beams [16], fractionally damped coupled system [17], fractional-order heat, wave and diffusion equations [18; 19], fractional order pine wilt disease model [20], fractional diabetes model [21] etc. Nowadays, the focus of the researchers is to develop different numerical and analytical techniques for the solution of fractional-order models. Therefore, different types of analytical and numerical methods have been developed and used for the solution of different fractional models. The analytical algorithm, the history of integral transform traced back to the time when [PERSON] started work an integral transform in 1780s and [PERSON] in 1822. Integral transformations are without question one of the most useful and effective methods in theoretical and applied mathematics, with numerous uses in quantum physics, mechanical engineering and several other areas of science. Moreover, the integral transform is used in chemistry, architecture, and other social sciences to evaluate various models [22]. In recent years, different integral transform such as Laplace transform [23; 24; 25], Fourier transform [26; 27], Hankel transform [28], Mellin transform [29], Z-transform [30], Wavelet transform [31], Elzaki transform [32; 33], Mahgoub transform [34], Aboodh transform [35], Mohand transform [36], Sumudu transform [37; 38], Hermite transform [39] etc have been used for the solution of different physical models. **Originality of the paper**: In this article, we have applied a new analytical technique, which is based on generalization of sumudu and laplace transform with Adomian decomposition method (ADM) to solve (2+time fractional-order) dimensional physical models. In the present research we have analyzed the fractional view of some important physical problems by using Shehu decomposition method (SDM). Some important fractional-order problems are solved, which provide the best information about the targeted physical problems as compare to integer-order problems solution. The results of the integer-order problem are compared with the fractional-order problems. In conclusion, in the present research work, we provided and improved the existing physical models of integer-order by using the idea of fractional calculus. The modified mathematical models of fractional-order derivative are solved by using a new and sophisticated analytical method. Moreover, the proposed analytical method has provided the solutions of the problems that have a very close contact with the exact solutions of the problems. The methodology can be extended towards other fractional-order partial differential equations, that are frequently occurred in science and engineering. The rest of the paper is organized as: In Section 2, we presented the basic definitions and theorem of the proposed method.