On Reaction-Diffusion Equation with Generalized Composite Fractional Derivative
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In this paper, we obtain the Sumudu transform of generalized composite fractional derivative and some lemmas related to inverse Sumudu transform. Further, we find solution of nonlinear reaction diffusion equation with generalized composite fractional derivative by applying the Sumudu and Fourier transforms.
References
-
Kuttler C. Reaction Diffusion Equation and their Applications on Bacterial Communication. Handbook of Statistics: Elsevier, 2017.
Google Scholar
1
-
Lan KQ, Wu JH. Travelling wavefronts of scalar reaction-diffusion equations with and without delays. Nonlinear Anal Real World Appl. 2013; 4(1): 173-188.
Google Scholar
2
-
Bessonov N, Bocharov G, Meyerhans A, Popov V, Volpert V. Nonlocal reaction–diffusion model of viral evolution: Emergence of virus strains. Mathematics. 2020; 8(1): 1-20.
Google Scholar
3
-
Grindrod P. Patterns and Waves: The theory and Applications of Reaction-Diffusion Equations (Oxford Applied Mathematics and Computing Science Series). The Clarendon Press Oxford, New York; 1996.
Google Scholar
4
-
Manne KK, Hurd AJ, Kenkre VM. Nonlinear waves in reaction-diffusion systems: The effect of transport memory. Phy Rev E. 2000; 61(4): 4177-4184.
Google Scholar
5
-
Saxena RK, Mathain AM, Haubold HJ. Reaction diffusion systems and nonlinear waves. Astrophys Space Sci. 2006; 305(3): 297-303.
Google Scholar
6
-
Alkahtani B, Gulati V, Kılıçman A, Application of Sumudu transform in generalized fractional reaction–diffusion equation. Int J Appl Comput Math. 2016; 2(3): 387-394.
Google Scholar
7
-
Fazli H, Bahrami F. On the steady solutions of fractional reaction-diffusion equations. Filomat. 2017; 31(6): 1655-1664.
Google Scholar
8
-
Viana A. A local theory for a fractional reaction-diffusion equation. Commun Contemp Math. 2019; 21(6): 1-26.
Google Scholar
9
-
Hilfer R. Applications of Fractional Calculus in Physics. World Scientific Publishing Company, Singapore- New jersey-Hong Kong; 2000.
Google Scholar
10
-
Kilbas AA, Srivastava HM, Trujillo J. Theory and Applications of Fractional Differential Equations. Elsevier Science, USA; 2006.
Google Scholar
11
-
Garg M, Manohar P, Chanchalani L, Alha S. On generalized composite fractional derivative. Walailak J Sci Technol. 2014; 11(12): 1069-1076.
Google Scholar
12
-
Anumaka MC. Analysis and applications of Laplace/Fourier transformation in electric circuit. Int J Res Rev Appl Sci. 2012; 12(2): 333-339.
Google Scholar
13
-
Marianito RR, Rogemar SM. An application of Mellin transform techniques to a black-scholes equation problem. Anal Appl. 2007; 5(1): 51-66.
Google Scholar
14
-
Mullineux N, Reed JR. On Hankel and Mellin transform. Int J Math Educ Sci Technol. 1978; 9(2): 139-145.
Google Scholar
15
-
Watugala GK. Sumudu transform: a new integral transform to solve differential equations and control engineering problems. Int J Math Educ Sci Technol. 1993; 24(1): 35-43.
Google Scholar
16
-
Belgacem FBM, Karaballi AA, Kalla SL. Analytical investigations of the Sumudu transform and applications to integral production equations. Math Probl Eng. 2003; 2003(3): 103-118.
Google Scholar
17
-
Belgacem FBM, Karaballi AA. Sumudu transform fundamental properties investigations and applications. Int J Stoch Anal. 2006; 2006(6): 1-23.
Google Scholar
18
-
Chaurasia VBL, Singh J. Application of Sumudu transform in Schödinger equation occurring in quantum mechanics. Appl Math Sci. 2010; 4(57): 2843-2850.
Google Scholar
19
-
Mullineux N, Reed JR. On Hankel and Mellin transform. Int J Math Educ Sci Technol. 1978; 9(2): 139-145.
Google Scholar
20
-
Metzler R, Klafter J. The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Phys Rep. 2000; 339(1): 1-77.
Google Scholar
21
-
Prabhakar TR. A singular integral equation with a generalized Mittag Leffler function in the kernel. Yokohama Math J. 1971; 19: 7-15.
Google Scholar
22
-
Katatbeh Q, Belgacem FBM. Applications of the Sumudu transform to fractional differentia equations. Nonlinear Stud. 2011; 18(1): 99-112.
Google Scholar
23
-
Gupta VG, Sharma B. Application of Sumudu transform in reaction-diffusion systems and nonlinear waves. Appl Math Sci. 2010; 4(9): 435-446.
Google Scholar
24