New Fractional Complex Transform for Conformable Fractional Partial Differential Equations

Y. Çenesiz; A. Kurt

doi:10.1515/jamsi-2016-0007

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New Fractional Complex Transform for Conformable Fractional Partial Differential Equations

Journal of Applied Mathematics, Statistics and Informatics

Volume 12 (2016): Issue 2 (December 2016)

By: Y. Çenesiz and A. Kurt

Open Access

|Dec 2016

Abstract

Conformable fractional complex transform is introduced in this paper for converting fractional partial differential equations to ordinary differential equations. Hence analytical methods in advanced calculus can be used to solve these equations. Conformable fractional complex transform is implemented to fractional partial differential equations such as space fractional advection diffusion equation and space fractional telegraph equation to obtain the exact solutions of these equations.

References

[1] S. Kazem, International Journal of Nonlinear Science 16(1), 3-11 (2013).
Search in Google Scholar Back to article
[2] I. Podlubny, Fractional Differential Equations, Academic Press (1999).
Search in Google Scholar Back to article
[3] K. Oldham and J. Spanier, The Fractional Calculus, Theory and Applications of Differentiation and Integration of Arbitrary Order, Academic Press (1974).
Search in Google Scholar Back to article
[4] K.S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, A Wiley-Interscience Publication (1993).
Search in Google Scholar Back to article
[5] A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier (2006).
Search in Google Scholar Back to article
[6] R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, Journal of Computational and Applied Mathematics 264, 65-70 (2014).10.1016/j.cam.2014.01.002
Search in Google Scholar Back to article
[7] M. Abu Hammad, R. Khalil, International Journal of Pure and Applied Mathematics 94(2), 215-221 (2014).10.12732/ijpam.v94i2.8
Search in Google Scholar Back to article
[8] A. Kurt, Y. Çenesiz, O. Tasbozan, Open Physics 13 (1), 355-360 (2015).10.1515/phys-2015-0045
Search in Google Scholar Back to article
[9] O. Tasbozan, Y. Çenesiz, A. Kurt, The European Physical Journal Plus, 131 (7), 244 (2016).10.1140/epjp/i2016-16244-x
Search in Google Scholar Back to article
[10] O.S. Iyiola, O.O. Gbenga, Pramana 85 (4), 567-575 (2015)10.1007/s12043-014-0915-2
Search in Google Scholar Back to article
[11] T. Abdeljawad, Journal of Computational and Applied Mathematics, 279,57-66 (2015).10.1016/j.cam.2014.10.016
Search in Google Scholar Back to article
[12] Z.B. Li, J.H. He, Nonlinear Sci. Lett. A,2(3), 121-126 (2010).
Search in Google Scholar Back to article
[13] Z.B. Li, W.H. Zhu, J.H. He, Thermal Science, 16(2), 335-338 (2012).10.2298/TSCI110503069L
Search in Google Scholar Back to article
[14] J.H. He, Z.B. Li, Thermal Science, 16(2), 331-334 (2012).10.2298/TSCI110503068H
Search in Google Scholar Back to article
[15] Z.B. Li, J.H. He, Mathematical and Computational Applications, 15(5), 970-973 (2010).10.3390/mca15050970
Search in Google Scholar Back to article
[16] G. Jumarie, J. Appl. Math. Computing 24(1-2), 31-48(2007).10.1007/BF02832299
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.1515/jamsi-2016-0007 | Journal eISSN: 1339-0015 | Journal ISSN: 1336-9180

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Language: English

Page range: 41 - 47

Published on: Dec 30, 2016

Published by: University of Ss. Cyril and Methodius in Trnava

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Conformable derivative,

conformable fractional complex transform,

fractional telegraph equation,

fractional advection diffusion equation

Related subjects:

Computer sciences,

Information technology,

Mathematics,

Logic and set theory,

Probability and statistics,

Applied mathematics

© 2016 Y. Çenesiz, A. Kurt, published by University of Ss. Cyril and Methodius in Trnava
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 12 (2016): Issue 2 (December 2016)