Identification of a time-dependent diffusivity coefficient in heat-like space-time fractional differential equations

Mine Aylin Bayrak; Ali Demir

doi:10.54559/jauist.1129786

Research Article

Identification of a time-dependent diffusivity coefficient in heat-like space-time fractional differential equations

Year 2022, Volume: 3 Issue: 2, 11 - 20, 31.12.2022

Mine Aylin Bayrak Ali Demir

https://doi.org/10.54559/jauist.1129786

Abstract

The goal of this research is to reveal the unknown time dependent diffusion coefficient in space-time fractional differential equations by means of fractional Taylor series method. Unlike most methods used in inverse problems, using no over-measured data is a substantial advantage of this method.
As a result, the unknown diffusion coefficient could be determined with high precision. Illustrative examples shows that the retrieved unknown coefficient and the solution of the problem are in a high agreement with the exact solution of the corresponding the inverse problems.

Keywords

space time fractional partial differential equations, fractional Taylor series method, Inverse problems

References

1. Kilbas, A.A. , Srivastava, H.M. and Trujillo, J.J. Theory and applications of fractional differential equations, Amsterdam: Elsevier, 2006.
2. } Podlubny, I. Fractional differential equation, San Diego, CA: Academic Press, 1999.
3. Sabatier, J., Agarwal, O.P. and Machado, J.A.T.(eds). Advances in fractional calculus: theoretical developments and applications in physics and engineering, Dordrecht: Springer, 2007.
4. Samko, S.G., Kilbas, A.A. and Marichev, O.I. Fractional integrals and derivatives theory and applications, Amsterdam: Gordon and Breach, 1993.
5. Odibat, Z. Approximations of fractional integrals and Caputo fractional derivatives. Appl. Math. Comput.178, 527-533, 2006.

Year 2022, Volume: 3 Issue: 2, 11 - 20, 31.12.2022

Mine Aylin Bayrak Ali Demir

https://doi.org/10.54559/jauist.1129786

Abstract

References

1. Kilbas, A.A. , Srivastava, H.M. and Trujillo, J.J. Theory and applications of fractional differential equations, Amsterdam: Elsevier, 2006.
2. } Podlubny, I. Fractional differential equation, San Diego, CA: Academic Press, 1999.
3. Sabatier, J., Agarwal, O.P. and Machado, J.A.T.(eds). Advances in fractional calculus: theoretical developments and applications in physics and engineering, Dordrecht: Springer, 2007.
4. Samko, S.G., Kilbas, A.A. and Marichev, O.I. Fractional integrals and derivatives theory and applications, Amsterdam: Gordon and Breach, 1993.
5. Odibat, Z. Approximations of fractional integrals and Caputo fractional derivatives. Appl. Math. Comput.178, 527-533, 2006.

There are 5 citations in total.

Details

Primary Language	English
Subjects	Engineering
Journal Section	Research & Review Articles
Authors	Mine Aylin Bayrak 0000-0001-7716-3455 Ali Demir 0000-0003-3425-1812
Publication Date	December 31, 2022
Published in Issue	Year 2022 Volume: 3 Issue: 2

Cite

APA	Bayrak, M. A., & Demir, A. (2022). Identification of a time-dependent diffusivity coefficient in heat-like space-time fractional differential equations. Journal of Amasya University the Institute of Sciences and Technology, 3(2), 11-20. https://doi.org/10.54559/jauist.1129786
AMA	Bayrak MA, Demir A. Identification of a time-dependent diffusivity coefficient in heat-like space-time fractional differential equations. J. Amasya Univ. Inst. Sci. Technol. December 2022;3(2):11-20. doi:10.54559/jauist.1129786
Chicago	Bayrak, Mine Aylin, and Ali Demir. “Identification of a Time-Dependent Diffusivity Coefficient in Heat-Like Space-Time Fractional Differential Equations”. Journal of Amasya University the Institute of Sciences and Technology 3, no. 2 (December 2022): 11-20. https://doi.org/10.54559/jauist.1129786.
EndNote	Bayrak MA, Demir A (December 1, 2022) Identification of a time-dependent diffusivity coefficient in heat-like space-time fractional differential equations. Journal of Amasya University the Institute of Sciences and Technology 3 2 11–20.
IEEE	M. A. Bayrak and A. Demir, “Identification of a time-dependent diffusivity coefficient in heat-like space-time fractional differential equations”, J. Amasya Univ. Inst. Sci. Technol., vol. 3, no. 2, pp. 11–20, 2022, doi: 10.54559/jauist.1129786.
ISNAD	Bayrak, Mine Aylin - Demir, Ali. “Identification of a Time-Dependent Diffusivity Coefficient in Heat-Like Space-Time Fractional Differential Equations”. Journal of Amasya University the Institute of Sciences and Technology 3/2 (December 2022), 11-20. https://doi.org/10.54559/jauist.1129786.
JAMA	Bayrak MA, Demir A. Identification of a time-dependent diffusivity coefficient in heat-like space-time fractional differential equations. J. Amasya Univ. Inst. Sci. Technol. 2022;3:11–20.
MLA	Bayrak, Mine Aylin and Ali Demir. “Identification of a Time-Dependent Diffusivity Coefficient in Heat-Like Space-Time Fractional Differential Equations”. Journal of Amasya University the Institute of Sciences and Technology, vol. 3, no. 2, 2022, pp. 11-20, doi:10.54559/jauist.1129786.
Vancouver	Bayrak MA, Demir A. Identification of a time-dependent diffusivity coefficient in heat-like space-time fractional differential equations. J. Amasya Univ. Inst. Sci. Technol. 2022;3(2):11-20.