On the Uniquness of Solutions of Linear Ordinary Fractional Differential Equations by Using Different Integral Transform Methods
AbstractThe main objective of this paper has to investigate the uniqueness of the solution of fractional differential equation by using different integral transforms, we applied Laplace transform, Elzaki transform and Sumudu transform on a linear ordinary fractional differential equation. The uniqueness of the solution is achieved in fractional differential equations by applying different integral transform methods.
B. J. West, M. Bolognab, and P. Grigolini, Physics of fractal operators, Springer, New York 2003.
K. S. Miller and B. Ross, An introduction to the fractional calculus and fractional differential equations, Wiley, New York 1993.
I. Podlubny, Fractional differential equations: An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Academic Press, New York 1999.
S.G. Samko, A.A. Kilbas, and O. I. Marichev, Fractional integrals and derivatives: theory and applications, Gordon and Breach, Amsterdam 1993.
S. Abbasbandy, J. Comput. Appl. Math. 207, 53 (2007).
G. Adomian, J. Math. Anal. Appl. 55, 441 (1976).
S.Momani and N. T. Shawagfeh, Appl.Math. Comput.182, 1083 (2006).
S. Kemple and H. Beyer, Global and causal solutions of fractional differential equations, Transform methods and special functions: Varna 96, Proceedings of 2nd international workshop (SCTP), Singapore, 96, 210 (1997).
L. Debnath and D. Bhatta, Integral transforms and their applications (second edition), Chapman and Hall/CRC, Boca Raton 2007.
B. Eugene, Mathematical Physics, Addison Wesley, 1968.
G. K. Watugala, “Sumudu transform: a new integral transform to solve differential equations and control engineering problems,” International Journal of Mathematical Education in Science and Technology, vol. 24, no. 1, pp. 35–43, 1993.
G. K.Watugala, “Sumudu transform—a new integral transform to solve differential equations and control engineering problems,” Mathematical Engineering in Industry, vol. 6, no. 4, pp.319–329, 1998.
T. M. Elzaki and S. M. Elzaki. “The new transform Elzaki Transform”, Global Journal of Pure and Applied Mathematics, 1: 57-64, 2011.
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