A new mathematical model of time fractional order heat equation and fractional order boundary condition have been constructed in the context of the generalized theory of thermo piezoelasticity. The governing equations have been applied to a semi infinite piezoelectric slab. The Laplace transform technique is used to remove the time-dependent terms in the governing differential equations and the...

In this paper, the differential transformation method (DTM) was applied to solve fuzzy fractional heat equations. The elementary properties of this method were given. The approximate and exact solutions of these equations were calculated in the form of series with easily computable terms. The proposed method was also illustrated by some examples. The results revealed that DTM is a highly effect...

Fractional calculus has many advantages. Under consideration of this paper is a (2+1)-dimensional non-linear local fractional heat conduction equation with arbitrary degree non-linearity. Backlund transformation reduced form the constructed by Painleve analysis. Based on transformation, some exact non-differentiable solutions are obtained. To gain more insights obtained solutions, two constrain...

Fractional calculus is the generalization of integer-order calculus to rational order. This subject has at least three hundred years of history. However, it was traditionally regarded as a pure mathematical field and lacked real world applications for a very long time. In recent decades, fractional calculus has re-attracted the attention of scientists and engineers. For example, many researcher...

We consider the fractional generalizations of equation that defines the medium mass. We prove that the fractional integrals can be used to describe the media with noninteger mass dimensions. Using fractional integrals, we derive the fractional generalization of the Chapman-Kolmogorov equation (Smolukhovski equation). In this paper fractional Fokker-Planck equation for fractal media is derived f...