
AIMS Mathematics, 2020, 5(2): 843855. doi: 10.3934/math2020057
Research article Special Issues
Export file:
Format
 RIS(for EndNote,Reference Manager,ProCite)
 BibTex
 Text
Content
 Citation Only
 Citation and Abstract
A new approach to solve CattaneoHristov diffusion model and fractional diffusion equations with HilferPrabhakar derivative
1 Amity Institute of information Technology, Amity University, Rajasthan, Jaipur303002, India
2 Department of Mathematics, University of Rajasthan, Jaipur302004, Rajasthan, India
3 Department of Mathematics, Amity University, Rajasthan, Jaipur303002, India
4 Department of Mathematics, Govt. P. G. College, Hisar, Haryana125001, India
Received: , Accepted: , Published:
Special Issues: Recent Advances in Fractional Calculus with Real World Applications
References
1. R. Garra, R. Gorenflo, F. polito, et al. HilferPrabhakar derivatives and some applications. Appl. Math. Comput., 242 (2014), 576589.
2. M. Caputo, M. Fabrizio, A new definition of fractional derivative without singular kernel. Progr. Fract. Differ. Appl., 1 (2015), 113.
3. J. Losada, J. J. Nieto, Properties of a new fractional derivative without singular kernel. Progr. Fract. Differ. Appl., 1 (2015), 8792.
4. J. Hristov, Approximate solutions to fractional subdiffusion equations. Eur. Phys. J. Spec. Top, 193 (2011), 229243.
5. J. Hristov, Transient heat diffusion with a nonsingular fading memory: From the Cattaneo constitutive equation with Jeffrey's Kernel to the CaputoFabrizio timefractional derivative. Therm. Sci., 20 (2016), 757762.
6. J. Hristov, Derivation of the fractional dodson equation and beyond: Transient di_usion with a nonsingular memory and exponentially fadingout diffusivity. Progr. Fract. Differ. Appl., 3 (2017), 116.
7. J. Hristov, On the AtanganaBaleanu derivative and its relation to the fading memory concept: The diffusion equation formulation, Fractional Derivatives with MittagLeffler Kernel, Stud. Syst. Decis. Control, Springer, Cham, 194 (2019), 175193.
8. J. Hristov, Steadystate heat conduction in a medium with spatial nonsingular fading memory derivation of caputofabrizio space fractional derivative from cattaneo concept with jeffrey's kernel and analytical solutions, Therm. Sci., 21 (2017), 827839.
9. I. Koca, A. Atangana, Solutions of cattaneohristov model of elastic heat diffusion with caputofabrizio and atanganabaleanu fractional derivatives, Therm. Sci., 21 (2017), 22992305.
10. B. S. T. Alkahtani, A. Atangana, A note on cattaneoHristov model with nonsingular fading memory. Therm. Sci., 21 (2017), 17.
11. J. Hristov, Multiple integralbalance method basic idea and an example with mullins model of thermal grooving. Therm. Sci., 21 (2017), 15551560.
12. J. Hristov, The nonlinear dodson diffusion equation: Approximate solutions and beyond with formalistic fractionalization. Math. Nat. Sci., 1 (2017), 117.
13. J. Hristov, Fourthorder fractional diffusion model of thermal grooving: integral approach to approximate closed form solution of the mullins model. Math. Modell. Nat. Phenom., 13 (2018), 6.
14. J. Hristov, Integralbalance solution to nonlinear subdiffusion equation. Front. Fractional. Calculus., 1 (2017), 71106.
15. J. Hristov, The heat radiation diffusion equation: Explicit analytical solutions by improved integralbalance method. Therm. Sci., 22 (2018), 777788.
16. J. Hristov, Integral balance approach to 1D spacefractional diffusion models, Mathematical Methods in Engineering, Nonlinear Syst. Complex. Springer Cham., 23 (2019), 111131.
17. J. Hristov, A transient flow of a nonnewtonian fluid modelled by a mixed timespace derivative: An improved integralbalance approach, Mathematical Methods in Engineering. Nonlinear Syst. Complex. Springer Cham., 24 (2019), 153174.
18. T. G. Myers, Optimal exponent heat balance and refined integral methods applied to stefan problems. Int. J. Heat Mass Transfer., 53 (2010), 11191127.
19. E. F. D. Goufo, Chaotic processes using the twoparameter derivative with nonsingular and nonlocal kernel: Basic theory and applications. Chaos: An Interdiscip. J. Nonlinear Sci., 26 (2016), 084305.
20. N. Sene, Exponential form for Lyapunov function and stability analysis of the fractional differential equations. J. Math. Comput. Sci., 18 (2018), 388397.
21. Tarig. M. Elzaki, The new integral transform "ELzaki Transform", Global J. Pure Appl Math., 7 (2011) 5764.
22. R. Gorenflo, F. Mainardi, Fractional calculus: Integral and differential equations of fractional order, A. Carpinteri and F. Mainardi (Editors): Fractals and Fractional Calculus in Continuum Mechanics, New York: SpringerVerlag Press (1997), 223276.
23. A. A. Kilbas, M. Saigo, R.K. Saxena, Generalized MittagLeffler function and generalized fractional calculus operators. Integr Transfor. Spec Funct., 15 (2004), 3149.
24. T. R. Prabhakar, A singular integral equation with a generalized MittagLeffler function in the kernel. Yokohama Math. J., 19 (1971), 75.
25. I. Podlubny, Matrix approach to discrete fractional calculus ii: Partial fractional differential equations. J. Comput. Phy., 228 (2009), 31313153.
26. Y. Ma, F. Zhang, C. Li, The asymptotics of the solutions to the anomalous diffusion equations. Comput. Math. Appl., 66 (2013), 682692.
27. V. Gill, J. Singh, Y. Singh, Analytical solution of generalized spacetime fractional advectiondispersion equation via coupling of Sumudu and Fourier transforms, Frontiers. Phy., 6 (2019), 16.
28. N. Sene, Stokes first problem for heated at plate with AtanganaBaleanu fractional derivative. Chaos Solitons Fractals, 117 (2018), 6875.
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)