In this article, the authors used two dimensional Laplace transform to solve non - homogeneous sub - ballistic fractional PDE and homogeneous systems of time fractional heat equations. Constructive examples are also provided.
A new method for the solution of linear constant coefficient fractional differential equations of any commensurate order based on the Laplace transforms of the fractional meta-trigonometric functions and the R-function is presented. The new method simplifies the solution of such equations. A simplifying characterization that reduces the number of parameters in the fractional meta-trigonometric functions is introduced.
This paper develops the fractional hyperbolic functions based on fractional generalization of the exponential function, the R-function. The fractional hyperbolic functions contain the traditional hyperbolic functions as proper subsets. Laplace transforms and various identities are derived for the new functions and are used to generate solution sets for various classes of fractional differential equations. Also developed are relationships between the R-function and the fractional hyperbolic functions.
We establish some important results about improper fuzzy Riemann integrals; we prove some properties of fuzzy Laplace transforms, which we apply for solving some fuzzy linear partial differential equations of first order, under generalized Hukuhara differentiability.
SOLVING SYSTEMS OF FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS VIA TWO DIMENSIONAL LAPLACE TRANSFORMS