Solution of Fractional Heat-Like and Fractional Wave-Like Equation by Using Modern Strategy
References
- Eltaib M Abd Elmohmoud, Mohamed Z Mohamed. Numerical treatment of some fractional nonlinear equations by Elzaki transform. Journal of Taibah University for Science.2022;16(1): 774-787.
- Metzler, R Nonnenmacher TF. Space-and time-fractional diffusion and wave equations fractional Fokker–Planck equations and physical motivation. Chem. Phys.2002;284:67–90.
- Metzler, R Klafter J. The random walk’s guide to anomalous diffusion A fractional dynamics approach. Phys Rep.2000; 339: 1–77.
- M Subramanian, M Manigandan, C Tunç, T N Gopal, J Alzabut. On system of nonlinear coupled differential equations and inclusions involving Caputo-type sequential derivatives of fractional order. Journal of Taibah University for Science.2022;16(1):1-23.
- Imran Talib, Ali Raza, Abdon Atangana, Muhammad Bilal Riaz. Numerical study of multi- order fractional differential equations with constant and variable coefficients. Journal of Taibah University for Science.2022;16(1):608-620.
- Jothimani, K Kaliraj, K Hammouch, Z Ravichandran C. New results on controllability in the framework of fractional integro differential equations with nondense domain. Eur Phys J Plus. 2019;134(9):441.
- Khan H, Shah R, Kumam P, Arif M. Analytical Solutions of Fractional- Order Heat and Wave Equations by the Natural Transform Decomposition Method. Entropy. 2019; 21: 597.
- Lei Y, Wang H, Chen X,Yang X, You Z, Dong S, Gao J. Shear property high-temperature rheological performance and low-temperature flexibility of asphalt mastics modified with bio-oil. Constr Build Mater. 2018;174:30–37.
- Zhang ZY. Symmetry determination and nonlinearization of a nonlinear time-fractional partial differential equation.Proc R Soc.2020;476:2019-0564.
- Mohamed Z Mohamed, Amjad E Hamza, Abdelilah Kamal H Sedeeg. An Efficient Approximate Solutions of the fractional coupled Burger’s equation by conformable double Sumudu transforms. Ain shams journal.2022;16: 101-879.
- Shah R, Khan H, Arif M, et al. Application of Laplace–Adomian decomposition method for the analytical solution of third-order dispersive fractional partial differential equations. Entropy. 2019;21(4):335.
- Shah HF, ur Rahman K, Shahzad M G. Numerical solution of fractional order smoking model via Laplace Adomian decomposition method. Alex Eng J. 2018;57(2):1061–1069.
- Rubbab Q, Nazeer M, Ahmad F, et al. Numerical simulation of advection– diffusion equation with Caputo Fabrizio time fractional derivative in cylindrical domains applications of pseudo-spectral collocation method. Alexandria Eng J. 2021;60(1):1731–1738.
- Agbata B C, Shior MM, Olorunni shola OA, Ezugorie IG, Obeng- Denteh. Analysis of Homotopy Perturbation Method (HPM) and its Application for Solving Infectious Disease Models. IJMSS 2021,9: 27-38.
- Hamoud A, Dawood L, Ghadle K, Atshan S. Usage of the modified variational iteration technique for solving Fredholm integro-differential equations. Int J Mech Prod Eng Res Dev.2019; 9(2):895–902.
- Osman M, Gong ZT, Mohammed A. Differential transform method for solving fuzzy fractional wave equation. J Comput Anal Appl.2021; 29(3):431–453.
- Omer Acan1, Omer Firat, Yildiray Keskin, Galip Oturanc. Conformable variational iteration method. NTMSCI.2017;5(1):172-178.
- G Adomian. A review of the decomposition method in applied mathematics. J Math Anal Appl.1988;135:501–544.
- G. Adomian Solving Frontier Problems of Physics The Decomposition method. Kluwer Academic Publishers Boston. 1994.
- S Momani, Z Odibat. Numerical comparison of methods for solving linear differential equations of fractional order. Chaos Solitons Fractals. 2007;31(5):1248–1255.
- Z Odibat, S Momani. Approximate solutions for boundary value problems of time-fractional wave equation. Appl Math Comput. 2006;181(1):767–774.
- V Marinca. An approximate solution for one-dimensional weakly nonlinear oscillations. J Nonlinear Sci Numer Simul.2002;3(2): 107–110.
- TH Hao. Search for variational principles in electrodynamics by Lagrange method. Int J Nonlinear Sci Numer Simul.2005;6(2): 209–210.
- Mustafa S. Hajira, Khan H, Shah R, Masood S. A Novel Analytical Approach for the Solution of Fractional-Order Diffusion-Wave Equations. Fractal Fract. 2021;5:206.
- Mainardi F. Fractional Calculus and Waves in Linear Viscoelasticity An Introduction to Mathematical Models. World Scientific Singapore. 2010.
- Anh VV, Leonenko NN. Harmonic analysis of random fractional diffusion–wave equations. Appl Math Comput.2003;141:77–85.
- Ali EJ. A new technique of initial boundary value problems using Adomian decomposition method. Int Math Forum. 2012;7:799–814.
- Mohamed Z Mohamed, Tarig M Elzaki. Applications of new integral transform for linear and nonlinear fractional partial differential equations. Journal of King Saud University – Science. 2020;32:544–549.
- Mustafa S, Hajira, Khan Hm Shah R, Masood S. A Novel Analytical Approach for the Solution of Fractional-Order Diffusion-Wave Equations. Fractal Fract. 2021;5:206.
- Alia A, Shaha K, Lib Y, Khana RA. Numerical treatment of coupled system of fractional order partial differential equations. J Math Comput Sci. 2019;19:74–85.
- Hassan Khan, Rasool Shah, Poom Kumam, and Muhammad Arif. Analytical Solutions of Fractional-Order Heat and Wave Equations by the Natural Transform Decomposition Method. mdpi journal entropy. 2019;21:597.
- S Sarwar, Salem Alkhalaf, S Iqbal, MA Zahid. A note on optimal homotopy asymptotic method for the solutions of fractional order heat- and wave-like partial differential equations. Computers & Mathematics with Applications. 2020;70(5):942-953.
- Shah R, Khan H, Mustafa S, Kumam P, Arif M. Analytical Solutions of Fractional-Order Diffusion Equations by Natural Transform Decomposition Method. Entropy,2019, 557.
- M A AL-Jawary. An Efficient Treatments For Linear And Nonlinear Heat-Like And Wave-Like Equations With Variable Coefficients. IOSR Journal of Mathematics.2015;11(4):01-13.
Language: English
Page range: 372 - 380
Submitted on: Sep 8, 2022
Accepted on: Feb 5, 2023
Published on: Jul 11, 2023
Published by: Bialystok University of Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
Related subjects:
© 2023 Mohamed Mohamed, Amjad Hamza, Tarig Elzaki, Mohamed Algolam, Shiraz Elhussein, published by Bialystok University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.