### Inverse Problem for Determination of An Unknown Coefficient in the Time Fractional Diffusion Equation

#### Abstract

#### Keywords

#### Full Text:

PDF#### References

O. Abu-Arqub, A. El-Ajou and S. Momani, Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations, J. Comput. Phys. 293 (2015), 385 – 399.

O. Abu-Arqub, A. El-Ajou, A. Bataineh and I. Hashim, A representation of the exact solution of generalized Lane-Emden equations using a new analytical method, Abstr. Appl. Analys. 10 (2013), doi:10.1155/2013/378593.

O. Abu-Arqub, A. El-Ajou, Z. Al-Zhour and S. Momani, Multiple solutions of nonlinear boundary value problems of fractional order: a new analytic iterative technique, Entropy 16 (2014), 471 – 493.

O. Abu-Arqub, Series solution of fuzzy differential equations under strongly generalized differentiability, J. Adv. Res. Appl. Math. 5 (2013), 31 – 52.

O. Abu-Arqub, Z. Abo-Hammour, R. Al-Badarneh and S. Momani, A reliable analytical method for solving higher-order initial value problems, Discr. Dyn. Nat. Soc. 12 (2013), doi:10.1155/2013/673829.

D. Baleanu, New Trends in Nanotechnology and Fractional Calculus Applications, Springer-Verlag (2009).

E.C. Baran and A.G. Fatullayev, Determination of an unknown source parameter in two dimensional heat equation, Appl. Math. Comput. 159 (2004), 881 – 886.

J.R. Cannon, Y. Lin and S. Xu, Numerical procedures for the determination of unknown coefficient in semi-linear parabolic differential equations, Inverse Problems 10 (1994), 227 – 243.

E. Cuesta and J. Finat, Image processing by means of a linear integro-differential equation, IASTED, 2003, pp. 438-442.

S.D. Eidelman and A.N. Kachubei, Cauchy problem for fractional diffusion equation, J. Comput Phys. 225 (2004), 1533 – 1552.

A. El-Ajou, O. Abu-Arqub and M. Al-Smadi, A general form of the generalized Taylor’s formula with some applications, Appl. Math. Comput. 256 (2015), 851 – 859.

A. El-Ajou, O. Abu-Arqub and S. Momani, Approximate analytical solution of the nonlinear fractional KdVBurgers equation: a new iterative algorithm, J. Comput. Phys. 293 (2015), 81 – 95.

A. El-Ajou, O. Abu-Arqub, S. Momani, D. Baleanu and A. Alsaedi, A novel expansion iterative method for solving linear partial differential equations of fractional order, Appl. Math. Comput. 257 (2015), 119 – 133.

A. El-Ajou, O. Abu-Arqub, Z. Al-Zhour and S. Momani, New results on fractional power series: theories and applications, Entropy 15 (2015), 5305 – 5323.

V. Isakov, Inverse parabolic problems with the final over determination, Comm. Pure Appl. Math. 44 (1991), 185 – 209.

A.A. Kilbas, H.M. Srivastava and J.J. Trujiilo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam (2006).

G.A. Kriegsmann and W.E. Olmstead, Source identification for the heat equation, Appl. Math. Lett. 1 (1988), 241 – 245.

V. Lakshmikantham, S. Leela and J.V. Devi, Theory of Fractional Dynamic systems, Cambridge Scientific Publishers (2009).

T.A.M. Langlands, B.I. Henry and S.L. Wearne, Fractional cable equation for anomalous electro diffusion in nerve cells: infinite domain solutions, J. Math. Biol. 59 (2009), 761 – 808.

Y. Lin and C. Xu, Finite difference/spectral approximations for the time-fractional diffusion equation, J. Comput. Phys. 225 (2007), 1533 – 1552.

F. Mainardi, The fundamental solutions for the fractional diffusion wave equation, Appl. Math. Lett. 9 (1996), 23 – 28.

I. Podlubny, Fractional Differential Equations, Academic, San Diego, CA (1999).

W. Rundel, The determination of a parabolic equation from initial and final data, Proc. Amer. Math. Sot. 99 (1987), 637 – 642.

J. Sabatier, O.P. Agrawal, T. Machado and J.A. (Eds.), Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, Dordrecht (2007).

K. Sakamoto and M. Yamamoto, Initial value/boundary value problems for fractional diffusion, J. Math. Anal. Appl. 382 (2011), 426 – 447.

S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional Integrals and Derivatives Theory and Applications, Gordon and Breach, Amsterdam (1993).

W.R. Schneider and W. Wyss, Fractional diffusion and wave equations, J. Math. Phys. 30 (1989), 134 – 144.

L. Yan, C.L. Fu and F.F. Dou, A computational method for identifying a spacewise dependent heat source, Commun. Numer. Methods Eng. 2008 doi:10.1002/cnm.1155

### Refbacks

- There are currently no refbacks.

eISSN 0975-8607; pISSN 0976-5905