Analytical solution of extended fractional space-time cable equation associated with Hilfer and Riemann-Liouville fractional derivatives

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Abstract

In this paper, we present a systematic investigation of a of the solution of generalized space-time fractional cable equation defined by (2.1) containing Riemann-Liouville and Hilfer fractional derivatives as the time  derivatives and  Riesz-Feller fractional derivative as the space derivative. The results are derived by the application of joint Laplace and Fourier transforms. The results are obtained in terms of the familiar H-function in a closed form. The moments of the solutions and their asymptotic behavior for small and large values of the argument are also obtained. The results are obtained in a compact form in terms of the Mittag-Leffler function and H-function. The results obtained by Can et al. [5] follow as special cases of our findings.

Keywords and Phrases

Mittag-Leffler function, Riesz-Feller space fractional derivative, Caputo fractional derivative, telegraph equation, Laplace transform, and Fourier transform.

A.M.S. subject classification

26A33, 44A10, 33C60.

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