Approximate solutions of linear timefractional differential equations
Volume 29, Issue 1, pp 6072
http://dx.doi.org/10.22436/jmcs.029.01.06
Publication Date: August 11, 2022
Submission Date: December 23, 2021
Revision Date: February 01, 2022
Accteptance Date: March 16, 2022
Authors
R. A. Oderinu
 Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, P.M.B 4000, Ogbomoso, Oyo Sate, Nigeria.
J. A. Owolabi
 Department of Mathematics, Bowen University, Iwo, P.M.B 284, Osun State, Nigeria.
M. Taiwo
 Department of Mathematics, Osun State College of Education, PMB 207, IlaOrangun, Osun State, Nigeria.
Abstract
In this research work, the numerical scheme for obtaining the linear timefractional differential equations was considered and the nature of these timefractional differential equations are in sense of Caputo. A theorem was proved to show the Kamal transform of \(n\)th order Caputo derivatives.
Finally, three problems were considered regarding the linear timefractional differential equations which presented that the convergence of the scheme provided in the research are of high accuracy for solving and linear fractional differential equations.
Share and Cite
ISRP Style
R. A. Oderinu, J. A. Owolabi, M. Taiwo, Approximate solutions of linear timefractional differential equations, Journal of Mathematics and Computer Science, 29 (2023), no. 1, 6072
AMA Style
Oderinu R. A., Owolabi J. A., Taiwo M., Approximate solutions of linear timefractional differential equations. J Math Comput SCIJM. (2023); 29(1):6072
Chicago/Turabian Style
Oderinu, R. A., Owolabi, J. A., Taiwo, M.. "Approximate solutions of linear timefractional differential equations." Journal of Mathematics and Computer Science, 29, no. 1 (2023): 6072
Keywords
 Kamal transform
 adomian polynomial
 linear timefractional differential equations
MSC
References

[1]
K. Abdelilah, S. Hassan, The new integral transform ”Kamal Transform”, Adv. Theor. Appl. Math., 11 (2016), 451458

[2]
F. H. Ahmed, Analytic approximate solutions for the 1D and 2D nonlinear fractional diffusion equations of Fisher type, C. R. Acad. Bulgare Sci., 73 (2020), 320330

[3]
H. O. AlHumedi, F. L. Hasan, The Numerical Solutions of Nonlinear TimeFractional Differential Equations by LMADM, Iraq. J. Sci., 2021 (2021), 1726

[4]
R. K. Bairwa, S. Karan, Analytical Solution of TimeFractional KlienGordon Equation by using LaplaceAdomian Decomposition Method, Ann. Pure Appl. Math., 24 (2021), 2735

[5]
M. S. H. Chowdhury, I. Hashim, Application of homotopyperturbation method to KleinGordon and sineGordon equations, Chaos Solitons Fractals, 39 (2009), 19281935

[6]
Y. M. Chu, H. B. Ehab, R. E. Essam, E. Abdelhalim, A. S. Nehad, Combination of Shehu decomposition and variational iteration transform methods for solving fractional third order dispersive partial differential equations, Numerical Methods for Partial Differential Equations, 2021 (2021), 12 pages

[7]
S. Frassu, C. van der Mee, G. Viglialoro, Boundedness in a nonlinear attractionrepulsion Keller–Segel system with production and consumption, J. Math. Anal. Appl., 504 (2021), 20 pages

[8]
H. Gandhi, A. Tomar, D. Singh, The Study of Linear and Nonlinear Fractional ODEs by Homotopy Analysis, In: Soft Computing, 2022 (2022), 407417

[9]
I. Hashim, O. Abdulaziz, S. Momani, Homotopy analysis method for fractional IVPs, Commun. Nonlinear Sci. Numer. Simul., 14 (2009), 674684

[10]
H. Jafari, V. DaftardarGejji, Solving linear and nonlinear fractional diffusion and wave equations by adomian decomposition, Appl. Math. Comput., 180 (2006), 488497

[11]
H. Jafari, V. DaftardarGejji, Solving a system of nonlinear fractional differential equations using Adomian decomposition, J. Comput. Appl. Math., 196 (2006), 644651

[12]
H. Jafari, C. M. Khalique, M. Nazari, Application of the Laplace decomposition method for solving linear and nonlinear fractional diffusion–wave equations, Appl. Math. Lett., 24 (2011), 17991805

[13]
H. Jafari, S. Seifi, Homotopy analysis method for solving linear and nonlinear fractional diffusionwave equation, Commun. Nonlinear Sci. Numer. Simul., 14 (2009), 20062012

[14]
A. Khalouta, A. Kadem, A new method to solve fractional differential equations: Inverse fractional Shehu transform method, Appl. Appl. Math., 14 (2019), 926941

[15]
H. Khan, U. Farooq, R. Shah, D. Baleanu, P. Kumam, M. Arif, Analytical solutions of (2+ time fractional order) dimensional physical models, using modified decomposition method, Appl. Sci., 10 (2020), 12 pages

[16]
H. Khan, S. Rasool, K. Poom, B. Dumitru, A. Muhammad, An efficient analytical technique, for the solution of fractionalorder telegraph equations, Mathematics, 7 (2019), 14 pages

[17]
H. Khan, S. Rasool, K. Poom, B. Dumitru, A. Muhammad, Laplace decomposition for solving nonlinear system of fractional order partial differential equations, Adv. Difference Equ., 2020 (2020), 18 pages

[18]
T. X. Li, N. Pintus, G. Viglialoro, Properties of solutions to porous medium problems with different sources and boundary conditions, Z. Angew. Math. Phys., 70 (2019), 18 pages

[19]
T. Li, G. Viglialoro, Boundedness for a nonlocal reaction chemotaxis model even in the attraction dominated regime, Differ. Integ. Equ., 34 (2021), 315336

[20]
C. P. Li, Y. H. Wang, Numerical algorithm based on Adomian decomposition for fractional differential equations, Comput. Math. Appl., 57 (2009), 16721681

[21]
S. T. MohyudDin, A. Yildirim, Variational iteration method for solving KleinGordon equations, J. Appl. Math. Stat. Inform., 6 (2010), 99106

[22]
S. Momani, K. AlKhaled, Numerical solutions for systems of fractional differential equations by the decomposition method, Appl. Math. Comput., 162 (2005), 13511365

[23]
S. Momani, Z. Odibat, Numerical comparison of methods for solving linear differential equations of fractional order, Chaos Solitons Fractals, 31 (2007), 12481255

[24]
S. Momani, O. Zaid, Analytical solution of a timefractional NavierStokes equation by Adomian decomposition method, Appl. Math. Comput., 177 (2006), 488494

[25]
J. A. Owolabi, O. E. Ige, E. I. Akinola, Application of Kamal Decomposition Transform Method in Solving Two Dimensional Unsteady Flow, Int. J. Differ. Equ., 14 (2019), 207214

[26]
J. A. Owolabi, R. A. Oderinu, Kamal Transform Based Analytical Solution of a Generalized Nonlinear HirotaSatsuma Coupled Equations, Asian J. Pure Appl. Math., 2021 (2021), 2029

[27]
S. S. Ray, A new approach for the application of Adomian decomposition method for the solution of fractional space diffusion equation with insulated ends, Appl. Math. Comput., 202 (2008), 544549

[28]
S. S. Ray, R. K. Bera, Analytical solution of a fractional diffusion equation by Adomian decomposition method, Appl. Math. Comput., 174 (2006), 329336

[29]
R. Shah, K. Hassan, A. Muhammad, K. Poom, Application of Laplace–Adomian decomposition method for the analytical solution of thirdorder dispersive fractional partial differential equations, Entropy, 21 (2019), 17 pages

[30]
R. Shah, K. Hassan, K. Poom, A. Muhammad, An analytical technique to solve the system of nonlinear fractional partial differential equations, Mathematics, 7 (2019), 15 pages

[31]
K. Shah, H. Khalil, R. A. Khan, Analytical solutions of fractional order diffusion equations by natural transform method, Iran. J. Sci. Technol. Trans. A Sci., 42 (2018), 14791490

[32]
S. C. Sharma, R. K. Bairwa, A reliable treatment of iterative Laplace transform method for fractional telegraph equations, Ann. Pure Appl. Math., 9 (2015), 8189

[33]
N. T. Shawagfeh, Analytical approximate solutions for nonlinear fractional differential equations, Appl. Math. Comput., 131 (2002), 517529

[34]
P. Verma, K. Manoj, An analytical solution of multidimensional space fractional diffusion equations with variable coefficients, Int. J. Model. Simul. Scient. Comput., 12 (2021), 13 pages

[35]
G. Wu, E. W. M. Lee, Fractional variational iteration method and its application, Phys. Lett. A, 374 (2010), 25062509

[36]
M. Zurigat, Solving nonlinear fractional differential equation using a multistep Laplace Adomian decomposition method, An. Univ. Craiova Ser. Mat. Inform., 39 (2012), 200210