On solutions for classes of fractional differential equations

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DOI:

https://doi.org/10.26637/mjm204/007

Abstract

We provide a new solution of diffusion fractional differential equation using fractal index method. Also we shall impose a new solution for Riccati equation of arbitrary order. The fractional operators are taken in sense of the Riemann-Liouville operators.

Keywords:

Fractional calculus

Mathematics Subject Classification:

34A12, 26A33
  • Pages: 411-418
  • Date Published: 01-10-2014
  • Vol. 2 No. 04 (2014): Malaya Journal of Matematik (MJM)

I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.

A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam, The Netherlands, 2006.

J. Sabatier, O. P. Agrawal, and J. A. Machado, Advance in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, Dordrecht, The Netherlands, 2007. DOI: https://doi.org/10.1007/978-1-4020-6042-7

V. Lakshmikantham, S. Leela, J. Vasundhara, Theory of Fractional Dynamic Systems. Cambridge Academic Publishers, Cambridge 2009.

D. Baleanu, B. Guvenc and J. A. Tenreiro, New Trends in Nanotechnology and Fractional Calculus Applications, Springer, New York, NY, USA, 2010. DOI: https://doi.org/10.1007/978-90-481-3293-5

P. R. Gordoa, A. Pickering, Z. N. Zhu, Bücklund transformations for a matrix second Painlev equation, Physics Letters A, 374 (34) (2010) 3422-3424. DOI: https://doi.org/10.1016/j.physleta.2010.06.034

R. Molliq, B. Batiha, Approximate analytic solutions of fractional Zakharov-Kuznetsov equations by fractional complex transform, International Journal of Engineering and Technology, 1 (1) (2012) 1-13.

R. W. Ibrahim, Complex transforms for systems of fractional differential equations, Abstract and Applied Analysis Volume 2012, Article ID 814759, 15 pages. DOI: https://doi.org/10.1155/2012/814759

S. Sivasubramanian, M. Darus, R. W. Ibrahim, On the starlikeness of certain class of analytic functions, Mathematical and Computer Modelling, vol. 54, no. 1-2(2011) pp. 112118. DOI: https://doi.org/10.1016/j.mcm.2011.01.042

R. W. Ibrahim, An application of Lauricella hypergeometric functions to the generalized heat equations, Malaya Journal of Matematik, 1(2014) 43-48. DOI: https://doi.org/10.26637/mjm201/006

J. R. Macdonald, L. R. Evangelista, E. K. Lenzi, and G. Barbero, J. Phys. Chem. C, 115(2011) 7648-7655. DOI: https://doi.org/10.1021/jp200737z

P. A. Santoro, J. L. de Paula, E. K. Lenzi, L. R. Evangelista, J. Chem. Phys. 135(114704)(2011) 1-5. DOI: https://doi.org/10.1063/1.3637944

J.T. Machado, V. Kiryakova, F. Mainardi, Commun. Nonlinear Sci. 16(2011) 1140- 1153. DOI: https://doi.org/10.1016/j.cnsns.2010.05.027

R. W. Ibrahim, On holomorphic solution for space- and time-fractional telegraph equations in complex domain, Journal of Function Spaces and Applications 2012, Article ID 703681, 10 pages. DOI: https://doi.org/10.1155/2012/703681

R. W. Ibrahim, Numerical solution for complex systems of fractional order, Journal of Applied Mathematics 2012, Article ID 678174, 11 pages. DOI: https://doi.org/10.1155/2012/678174

K. Diethelm, The Analysis of Fractional Differential Equations, Springer-Verlag Berlin Heidelberg, 2010. DOI: https://doi.org/10.1007/978-3-642-14574-2

S. Zhang, H.Q. Zhang, Fractional sub-equation method and its applications to nonlinear fractional PDEs, Phys. Lett. A, 375 (2011) 1069-1073. DOI: https://doi.org/10.1016/j.physleta.2011.01.029

A. N. Kochubei, The Cauchy problem for evolution equations of fractional order, Differential Equations 25 $(1989) 967-974$

A. N. Kochubei, Diffusion of fractional order, Differential Equations 26 (1990) 485-492.

R. Metzler, J. Klafter, The random walks guide to anomalous diffusion: A fractional dynamics approach. Phys. Rep. 339 (2000) 1-77. DOI: https://doi.org/10.1016/S0370-1573(00)00070-3

G. Zaslavsky, Fractional kinetic equation for Hamiltonian chaos. Chaotic advection, tracer dynamics and turbulent dispersion. Phys. D $76(1994)$ 110-122. DOI: https://doi.org/10.1016/0167-2789(94)90254-2

F. Mainardi, G. Pagnini and R. Gorenflo; Some aspects of fractional diffusion equations of single and distributed order, App. Math. Compu., 187( 1) (2007) 295-305. DOI: https://doi.org/10.1016/j.amc.2006.08.126

F. Mainardi, A. Mura, G. Pagnini and R. Gorenflo; Sub-diffusion equations of fractional order and their fundamental solutions, Invited lecture by F. Mainardi at the 373. WEHeraeus- Seminar on Anomalous Transport: Experimental Results and Theoretical Challenges, Physikzentrum Bad-Honnef (Germany), 12-16 July 2006.

F. Black, M. S. Scholes, The pricing of options and corporate liabilities, J. Polit. Econ. 81 (1973) $637-654$. DOI: https://doi.org/10.1086/260062

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Published

01-10-2014

How to Cite

Rabha W. Ibrahim, and S. K. Elagan. “On Solutions for Classes of Fractional Differential Equations”. Malaya Journal of Matematik, vol. 2, no. 04, Oct. 2014, pp. 411-8, doi:10.26637/mjm204/007.

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Vol. 2 No. 04 (2014): Malaya Journal of Matematik (MJM)

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