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Articles

Recovering space-dependent source for a time-space fractional diffusion wave equation by fractional Landweber method

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Pages 990-1011 | Received 01 Nov 2019, Accepted 17 Aug 2020, Published online: 06 Sep 2020

References

  • Chen W, Holm S. Physical interpretation of fractional diffusion wave equation via Lossy media obeying frequency power law; 2003. Available from: https://arxiv.org/abs/math-ph/0303040.
  • Sakamoto K, Yamamoto M. Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems. J Math Anal Appl. 2011;382:426–447. doi: 10.1016/j.jmaa.2011.04.058
  • Du R, Cao WR, Sun ZZ. A compact difference scheme for the fractional diffusion-wave equation. Appl Math Model. 2010;34:2998–3007. doi: 10.1016/j.apm.2010.01.008
  • Agrawal OP. Solution for a fractional diffusion wave equation defined in a bounded domain. Nonlinear Dyn. 2002;29:145–155. doi: 10.1023/A:1016539022492
  • Jiang H, Liu F, Turner I, et al. Analytical solutions for the multi-term time fractional diffusion wave/diffusion equations in a finite domain. Comput Math Appl. 2012;64:3377–3388. doi: 10.1016/j.camwa.2012.02.042
  • Chen A, Li C. Numerical solution of fractional diffusion wave equation. Numer Funct Anal Optim. 2016;37:19–39. doi: 10.1080/01630563.2015.1078815
  • Dai H, Wei L, Zhang X. Numerical algorithm based on an implicit fully discrete local discontinuous Galerkin method for the fractional diffusion wave equation. Numer Algorithms. 2014;67:845–862. doi: 10.1007/s11075-014-9827-y
  • Zhou Y, He JW, Ahmad B, et al. Existence and regularity results of a backward problem for fractional diffusion equations. Math Methods Appl Sci. 2019;42(18):6775–6790. doi: 10.1002/mma.5781
  • Tuan NH, Huynh LN, Ngoc TB, et al. On a backward problem for nonlinear fractional diffusion equations. Appl Math Lett. 2019;92:76–84. doi: 10.1016/j.aml.2018.11.015
  • Wei T, Zhang Y. The backward problem for a time-fractional diffusion-wave equation in a bounded domain. Comput Math Appl. 2018;75:3632–3648. doi: 10.1016/j.camwa.2018.02.022
  • Huynh LN, Zhou Y, Oregan D, et al. Fractional Landweber method for an initial inverse problem for time-fractional wave equation. Appl Anal. 2019; Available From: https://doi.org/10.1080/00036811.2019.1622682.
  • Yang F, Zhang Y, Li XX. Landweber iterative method for identifying the initial value problem of the time-space fractional diffusion wave equation. Numer Algorithms. 2020;83:1509–1530. doi: 10.1007/s11075-019-00734-6
  • Jiang SZ, Liao KF, Wei T. Inversion of the initial value for a time-fractional diffusion wave equation by boundary data. Comput Methods Appl Math. 2020;20:109–120. doi: 10.1515/cmam-2018-0194
  • Xian J, Wei T. Determination of the initial data in a time fractional diffusion wave problem by a final time data. Comput Math Appl. 2019;78(8):2525–2540. doi: 10.1016/j.camwa.2019.03.056
  • Liao KF, Li YS, Wei T. The identification of the time dependent source term in time fractional diffusion wave equations. East Asian J Appl Math. 2019;9(2):330–354. doi: 10.4208/eajam.250518.170119
  • Gong X, Wei T. Reconstruction of a time-dependent source term in a time fractional diffusion equation. Inverse Probl Sci Eng. 2019;27:1577–1594. doi: 10.1080/17415977.2018.1539481
  • Siskova K, Slodicka M. Recognition of a time-dependent source in a time fractional diffusion wave equation. Appl Numer Math. 2017;121:1–17. doi: 10.1016/j.apnum.2017.06.005
  • Lopushansky A, Lopushanska H. Inverse source Cauchy problem for a time fractional diffusion wave equation with distributions. Electron J Differ Equ. 2017;2017:1–14. doi: 10.1186/s13662-016-1057-2
  • Kian Y, Oksanen L, Soccorsi E, et al. Global uniqueness in an inverse problem for time fractional diffusion equations. J Differ Equ. 2018;264(2):1146–1170. doi: 10.1016/j.jde.2017.09.032
  • Yang F, Liu X, Li XX, et al. Landweber iterative regularization method for identifying the unknown source of the time fractional diffusion equation. Adv Differ Equ. 2017;2017:149. doi: 10.1186/s13662-017-1205-3
  • Yan XB, Wei T. Determine a space-dependent source term in a time fractional diffusion wave equation. Acta Appl Math. 2020;165:163–181. doi: 10.1007/s10440-019-00248-2
  • Klann E, Ramlau R. Regularization by fractional filter methods and data smoothing. Inverse Prob. 2008;24(2):045005. doi: 10.1088/0266-5611/24/2/025018
  • Han YZ, Xiong XT, Xue XM. A fractional Landweber method for solving backward time fractional diffusion problem. Comput Math Appl. 2019;78:81–91. doi: 10.1016/j.camwa.2019.02.017
  • Tatar S, Tnaztepe R, Ulusoy S. Determination of an unknown source term in a space-time fractional diffusion equation. Fract Calc Appl Anal. 2015;6(1):83–90.
  • Tatar S, Tnaztepe R, Ulusoy S. Simultaneous inversion for the exponents of the fractional time and space derivative in the space-time fractional diffusion equation. Appl Anal. 2016;95(1):1–23. doi: 10.1080/00036811.2014.984291
  • Tatar S, Ulusoy S. An inverse source problem for a one-dimensional space-time fractional diffusion equation. Appl Anal. 2015;94(11):2233–2244. doi: 10.1080/00036811.2014.979808
  • Podlubny I. Fractional differential equations. San Diego (CA): Academic Press; 1999.
  • Kilbas A, Srivastava H, Trujillo J. Theory and applications of fractional differential equations. Vol. 204. Amsterdam: Elsevier; 2006. p. 2453–2461.
  • Engl HW, Hanke M, Neubauer A. Regularization of inverse problems, mathematics and its applications. Dordrecht: Kluwer Academic Publishers Group; 1996.
  • Li YS, Wei T. An inverse time dependent source problem for a time space fractional diffusion equation. Appl Math Comput. 2018;336:257–271.
  • Zhang Y, Sun Z. Alternating direction implicit schemes for the two-dimensional fractional sub-diffusion equation. J Comput Phys. 2011;230(24):8713–8728. doi: 10.1016/j.jcp.2011.08.020

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