On Aboodh transform for fractional differential operator

Tukaram G. Thange; Anantha R. Gade

doi:10.26637/MJM0801/0038

Abstract

In this paper we introduce Aboodh transform for the different fractional differential operators. Using this transform solution of initial value fractional order differential equation is given and finally, we discuss some illustrative examples on the above results

Keywords:

Aboodh Transform, Riemann-Liouville and Caputo fractional derivative,, Mittag-Leffler Function, Fractional differential equations

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

Tukaram G. Thange Department of Mathematics, Yogeshwari Mahavidyalaya Ambajogai, Beed-431517, Maharashtra, India.
Anantha R. Gade Department of Mathematics, M.S.P. Mandals Arts, Science & Commerce, Dharur-431124, Maharashtra, India.

Pages: 225-229
Date Published: 01-01-2020
Vol. 8 No. 01 (2020): Malaya Journal of Matematik (MJM)

V. Lakshmikantam, A. S. Vatsala, Basic theory of fractional diffe-rential equation, Nonlinear Analysis, 69(8)(2008), 2677-2682.

ElifDemirci, Nuri Ozalp, A methods for solving differential equation of fractional order, Journal of Computational and Applied Mathematics, 236(11)(2012), 27542762.

Khalil Suliman Aboodh, The new integral transform Aboodh transform, Global Journal of Pure and Applied Mathematics, 9(1)(2013), 35-43.

Mountassir H. Cherif and DjelloulZiane, Variational iteration method combined with new transform to solve fractional partial differential equation, Universal Journal of Mathematics and Applications, 1(2)(2008), 28-38.

Mohand M. AbdelrahimMahgoub and Abdelbagy A. Alshikh, On the relationship between aboodh transform and new integral transform Z-transform, Mathematical Theory and Modelling, 6(9)(2016), 113-119.

K. S. Aboodh, Abdullahi Idris and R. I. Nurudeen, On the Aboodh transform connection which some famous integral transformer, International Journal in Engineering and Information System, 1(2017), 1024-1030.

Sudhanshu Agrawal, Nidhi Sharma, Raman Chauhan, Application of Aboodh transform for solving linear Voltteraintegro differential equation of second kind, International Journal of Research in Advanced Technology, 6(6)(2018), 13-29.

N. Engheta, On fractional calculus and fractional multipoles in elec-tromagnetism, IEEE Trans. Antennas Propagations, 16(1)(1996), 554-566.

F. Mainardi, Fractional calculus: in basic problems in continuum and statistical mechanics, Fractals and Fractional Calculus in Continuum Mechanics, 1(1997), 291-348.

V. G Ychuk, B. Datsko, V. Meleshko, Mathematical modelling on time fractional reaction diffusion system, $J$. Comput. Appl. Math., 220(1)(2008), 215-225.

F. B. M.Duarte, J. A. T. Machado, Chaotic phenomenon and frac-tional dynamics in the trajectory control of redundant manipulator, Nonlinear Dynamics, 29(1)(2002), $343-362$.

Li Kexue, Peng Jigen, Laplace transform of fractional differential equation, Applied Mathematics Letters, 24(2011), 2019-2023.

QutaibehDeebKatatbeh, Fethi Bin Muhammad Belgacem, Application of Sumudu transform to fractional differential equations, Nonlinear Studies, 18(2011), 99112.

Rachid Belgacem, Dumitru Beleanu, Ahmed Bokhari, Shehu Transform and applications to Caputo fractional Differential Equation, International Journal of Analysis and Applications, 17(6)(2019), 917-927.

R. Khandelwal, P. Choudhary and Y. Khandelwal, Solution of fractional order differential Equation by Kamal Transform, International Journal of Statistics and Applied Mathematics, 3(2018), 279-284.

Zain Ul Abadin Zafar, Application of Z-transform method on some fractional differential equations, International Journal of Advance Engineering and Global Technology, 4(2016), 14-23.