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Numerical solution of a time-fractional inverse source problem | ||
| Journal of Hyperstructures | ||
| دوره 7، Spec. 2nd CSC2017، شهریور 2018، صفحه 14-26 اصل مقاله (733.05 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2018.2686 | ||
| نویسندگان | ||
| Afshin Babaei* 1؛ Seddighe Banihashemi2 | ||
| 1UniverDepartment of Mathematics, University of Mazandaran, P.O.Box 47416-95447, Babolsar, Iransity of Mazandaran | ||
| 2Department of Mathematics, University of Mazandaran, P.O.Box 47416-95447, Babolsar, Iran | ||
| چکیده | ||
| In this paper, an inverse problem of determining an unknown source term in a time-fractional diffusion equation is investigated. This inverse problem is severely ill-posed. For this reason, a mollification technique is used to obtain a regularized problem. Afterwards, a finite difference marching scheme is introduced to solve this regularized problem. The stability of numerical solution is investigated. Finally, two numerical examples are presented to illustrate the validity and effectiveness of the proposed method. | ||
| کلیدواژه‌ها | ||
| Ill-posed problem؛ Caputo’s fractional derivative؛ Mollification؛ Marching scheme | ||
| مراجع | ||
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[1] K.B. Oldham, J. Spanier, The Fractional Calculus: Theory and Application of Differentiation and Integration to Arbitrary Order, Academic Press, New York,(1974). [2] I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999. [3] K.S. Cole, Electric conductance of biological systems, in: Proc. Cold Spring Harbor Symp. Quant. Biol, Cold Spring Harbor, New York (1993), 107–116. [4] R. Metzler, J. Klafter, The random walks guide to anomalous diffusion: a fractional dynamics approach, Phys Rep 339(1) (2000), 1-77. [5] M. Raberto, E. Scalas, F. Mainardi, Waiting-times and returns in high-frequency financial data: an empirical study, Physica A: Statistical Mechanics and its Ap-plications 314 (1) (2002), 749-755. [6] Schumer. R., Meerschaert. M. and Baeumer. B., Fractional advectiondispersion equations for modeling transport at the earth surface, J. Geophys. Res.: Ea. Surf., 114 (2009) No. 4, Article ID F00A07. [7] D. Baleanu, J.A. Tenreiro Machado, A.C.J. Luo, Fractional dynamics and con-trol, Springer, New York, 2012. [8] B. Guo, X. Pu, F. Huang, Fractional partial differential equations and their numerical solutions, World scientific, Singapore, (2015). [9] A. Babaei, S. Banihashemi, A Stable Numerical Approach to Solve a Time-Fractional Inverse Heat Conduction Problem, Iranian Journal of Science and Technology, Transactions A: Science (2017), DOI: 10.1007/s40995-017-0360-4. [10] S. R. Arridge and J. C. Schotland, Optical tomography: forward and inverse problems, Inverse Problems, 25 (2009). [11] J.V. Beck, B. Blackwell and C.R. Clair, Inverse Heat Conduction: Ill-Posed Problems, New York, (1985). [12] M. Prato, L. Zanni, Inverse problems in machine learning: an application to brain activity interpretation, Journal of Physics: Conference Series 135 (2008) 012085. [13] B. Jin, W. Rundell, A tutorial on inverse problems for anomalous diffusion pro-cesses, Inverse problems, 31 (2015) 035003. [14] D. A. Murio, Time fractional IHCP with Caputo fractional derivatives, Comput-ers and Mathematics with Applications, 56 (2008), 2371-2381. [15] A. Taghavi, A. Babaei, A. Mohammadpour, A stable numerical scheme for a time fractional inverse parabolic equation, Inverse Probl Sci Eng. 25 (10) (2017),1474–1491. [16] D.A. Murio, Mollification and space marching, in: K. Woodbury (Ed.), Inverse Engineering Handbook, CRC Press, Boca Raton, FL, (2002). [17] D.A. Murio, On the stable numerical evaluation of Caputo fractional derivatives, Computers and Mathematics with Applications, 51, (2006), 1539–1550. | ||
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