×

Hybrid method for solution of fractional order linear differential equation with variable coefficients. (English) Zbl 1401.65090

Summary: In this paper, we proposed a new analytical hybrid methods for the solution of conformable fractional differential equations (CFDE), which are based on the recently proposed conformable fractional derivative (CFD) in [R. Khalil et al., J. Comput. Appl. Math. 264, 65–70 (2014; Zbl 1297.26013)]. Moreover, we use the method of variation of parameters and reduction of order based on CFD, for the CFDE. Furthermore, to show the efficiency of the proposed analytical hybrid method, some examples are also presented.

MSC:

65L99 Numerical methods for ordinary differential equations
34A08 Fractional ordinary differential equations

Citations:

Zbl 1297.26013
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] A. Kilbas, H. Srivastava, and J. Trujillo, Theory and applications of fractional differential equations. Math. Studies. Northholland, New York, 2006. · Zbl 1092.45003
[2] Y. Cenesiz and A. Kurt, The solution of time fractional wave equation with conformable fractional derivative definition, J. New Theory. (2014), 195-198.
[3] A. Gokdogan, E. Unal and E. Celik, Conformable fractional Bessel equation and Bessel function (2015), 1-12.
[4] A. Atangana, D. Baleanu and A. Alsaedi, New properties of conformable derivative, open mathematics (2015), 13, 889-989. · Zbl 1354.26008
[5] A. Gökdoğan, E. Ünalb and E. Çelik, Existence and uniqueness theorems for sequential linear conformable fractional differential equations, preprint arXiv:1504.02016 (2015).
[6] K. S. Miller and B. Ross, An introduction to fractional calculus and fractional differential equations, John Wiley and Sons, New York, 1993. · Zbl 0789.26002
[7] I. Podlubny, Fractional differential equation, Academic Press, U.S.A., 1999. · Zbl 0893.65051
[8] R. Khalil, M. Al Horani, A. Yusuf and M. Sababhed, A New definition of fractional derivative, J. Comput. Appl. 264 (2014), 65-70. · Zbl 1297.26013
[9] U. N. Katugampola, A new fractional derivative with classical properties, J. Am. Math. Soc. (2014).
[10] R. Khalil and M. Abu-Hammad, Abel’s formula and Wronskian for conformable fractional differential equations, Int. J. Differential Eq. and Appl. 13 (3) (2014), 177-183. · Zbl 1321.34008
[11] T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math. 279 (2015), 57-66. · Zbl 1304.26004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.