Joint Laplace-Fourier Transforms For Fractional PDEs

Year 2014, Volume: 2 Issue: 3, 166 - 177, 01.12.2014

Arman Aghili Homa Zeinali

Abstract

In this paper, the authors implemented one dimensional Laplace transform to evaluate certain integrals, series and solve non homogeneous fractional PDEs. Illustrative examples are also provided. The results reveal that the integral transforms are very effective and convenient

Keywords

Laplace transform, Bessel’s functions; Parabolic cylindrical function; Wave equation; Caputo fractional derivative

1. Introduction and Notations

Abstract

References

• A.Aghili, H.Zeinali, Integral transform method for solving Volterra Singular integral equations and non homogenous time Fractional PDEs. Gen.Math.Notes, Vol.14, No.1, January 2013, pp.6-20.
• A.Aghili, H.Zeinali, Integral transform methods for solving fractional PDEs and evaluation of certain integrals and series. Intern journal of physics and mathematical sciences, Vol.2(4),2012.
• V.A. Ditkin. and Prudnikov,A.P.: Operational Calculus In Two Variables and Its Application ,Pergamon Press, New York,1962.
• W.W.Bell, Special functions for scientists and engineers, D.Van Nostrand company LTD, Canada, 1968.
• D.G.Duffy, Transform methods for solving partial differential equations, Chapman and Hall/CRC NewYork,2004.
• H.J.Glaeske, A.P.Prudnikov, K.A.Skornik, Operational calculus and related topics, Chapman and Hall/CRC, USA, 2006.
• I. Podlubny, Fractional differential equations, Academic Press, San Diego, CA,1999.
• A.. D. Polyanin, A. V. Manzhirov, Handbook of integral equations, Chapman and Hall/CRC, USA, 2008.