Fractional Relaxation and Fractional Oscillation Models Involving Erdélyi-Kober Integrals

Author:

Concezzi Moreno1,Garra Roberto2,Spigler Renato1

Affiliation:

1. Department of Mathematics and Physics Roma Tre University 1, Largo S. Leonardo Murialdo 00146 Rome, ITALY

2. Department of Statistical Sciences “Sapienza” University of Rome 5, P. le Aldo Moro 00185 Rome, ITALY

Abstract

Abstract We consider fractional relaxation and fractional oscillation equations involving Erdélyi-Kober integrals. In terms of the Riemann-Liouville integrals, the equations we analyze can be understood as equations with time-varying coefficients. Replacing the Riemann-Liouville integrals with Erdélyi-Kober-type integrals in certain fractional oscillation models, we obtain some more general integro-differential equations. The corresponding Cauchy-type problems can be solved numerically, and, in some cases analytically, in terms of the Saigo-Kilbas Mittag-Leffler functions. The numerical results are obtained by a treatment similar to that developed by K. Diethelm and N.J. Ford to solve the Bagley-Torvik equation. Novel results about the numerical approach to the fractional damped oscillator equation with time-varying coefficients are also presented.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

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