First Aboodh Transform of Fractional Order and Its Properties

Suliman Alfaqeih, T. ÖZIS

Abstract


In this paper, we propose definitions of a fractional first Aboodh transform of order α, where α ϵ [0, 1], for a functions which are fractional differentiable. We then present some main properties of this transform. Furthermore, we prove some related theorems.

Keywords


Aboodh transform , Laplace transform , double Aboodh transform , Mittag leffler function .

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References


Khalaf R.F. and Belgacem F.B.M., Extraction of the Laplace, Fourier, and Mellin Transforms from the Sumudu transform, AIP Proceedings, 1637, 1426 (2014

Watugula G.K., Sumudu transform: a new integral transform to solve differential equations and control engineering problems, International Journal of Mathematical Education in Science and Technology, 24(1) (1993) 35-43

Elzaki T.M., The new integral transform "Elzaki transform", Global Journal of Pure and Applied Mathematics, 7(1) (2011) 57-64

Khan Z.H., and Khan W.A., Natural transform-properties and applications, NUST Journal of Engineering Sciences, 1(2008) 127-133

D.G. Duff, Transform Methods for Solving Partial Differential Equations, Chapman and Hall/CRC, Boca Raton, F.L, 2004.

Hassan Eltayeb and Adem kilicman, A Note on the Sumudu Transforms and differential Equations, Applied Mathematical Sciences, VOL, 4, 2010, no. 22, 1089-1098

Mohand, M, Khalid Suliman Aboodh,& Abdelbagy, A. On the Solution of Ordinary Differential Equation with Variable Coefficients using Aboodh Transform, Advances in Theoretical and Applied Mathematicsb ISSN 0973-4554 Volume 11, Number 4 (2016), pp. 383-389.

Mohand M. Abdelrahim Mahgob “ Homotopy Perturbation Method And Aboodh Transform For Solving Sine –Gorden And Klein – Gorden Equations” International Journal of Engineering Sciences & Research Technology, 5 (10): October, 2016

K.S.Aboodh, Application of new transform "Aboodh transform" to Partial Differential Equations, Global Journal of Pure and Applied Mathematics, 10(2) (2014) 249-254

Khalid Suliman Aboodh, The New Integral Transform ''AboodhTransform''GlobalJournalofPure and Applied Mathematics ISSN 0973-1768 Volume 9, Number 1 (2013), pp. 35-43.

R. I. Nuruddeen and K. S. Aboodh, Analytical Solution For Time-Fractional Diffusion Equation By Aboodh Decomposition Method, Int. J. Math. And App., 5 (1–A) (2017), 115-122.

I. Podlubny, Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Vol. 198 (Academic press, 1998).

S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional integrals and derivatives (Theory and Applications, Gordon and Breach, Yverdon, 1993).

Guy Jumarie Laplace’s transform of fractional order via the Mittag–Leffler function and modified Riemann–Liouville derivative


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