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Solutions of Analytical Systems of Partial Differential Equations

Trenčevski, K. (1995)

Serdica Mathematical Journal

In this paper are examined some classes of linear and non-linear analytical systems of partial differential equations. Compatibility conditions are found and if they are satisfied, the solutions are given as functional series in a neighborhood of a given point (x = 0).

Solutions of Fractional Diffusion-Wave Equations in Terms of H-functions

Boyadjiev, Lyubomir, Al-Saqabi, Bader (2012)

Mathematica Balkanica New Series

MSC 2010: 35R11, 42A38, 26A33, 33E12The method of integral transforms based on joint application of a fractional generalization of the Fourier transform and the classical Laplace transform is utilized for solving Cauchy-type problems for the time-space fractional diffusion-wave equations expressed in terms of the Caputo time-fractional derivative and the Weyl space-fractional operator. The solutions obtained are in integral form whose kernels are Green functions expressed in terms of the Fox H-functions....

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