Conformable Fractional Elzaki Decomposition Method of Conformable Fractional Space-Time Fractional Telegraph Equations

Year 2022, Volume: 4 Issue: 2, 42 - 55, 31.12.2022

Halil Anaç

https://doi.org/10.54286/ikjm.1178988

Cited By: 2

Abstract

Conformable space-time fractional linear telegraph equations are examined using a new method known as conformable fractional Elzaki decomposition method. The suggested method combines the Adomian decomposition method with the conformable fractional Elzaki transform. It is found that numerical simulations confirm the effectiveness and reliability of the proposed method.

Keywords

Conformable fractional Elzaki decomposition method, conformable time-fractional telegraph equation, conformable Elzaki transform

References

• [1] Shah R., Khan H., Baleanu, D., (2019) Fractional Whitham–Broer–Kaup equations within modified analytical approaches, Axioms, 8(4), 125.
• [2] Miller K.S., Ross B., (1993) An introduction to the fractional calculus and fractional differential equations, John Wiley &Sons, New York.
• [3] Kilbas A. A., Srivastava H. M., Trujillo J. J., (2006) Theory and applications of fractional differential equations, Elsevier, London.
• [4] Ortigueir, M. D. (2011) Fractional calculus for scientists and engineers, Springer Science & Business Media, London.
• [5] Atangana, A., Baleanu, D., Alsaedi A. (2015) New properties of conformable derivative, Open Math, 13(1), 889-898.
• [6] Momani, S., Shawagfeh N. (2006) Decomposition method for solving fractional Riccati differential equations, Appl Math Comput, 182(2), 1083-1092.
• [7] Kurt A., Rezazadeh H., Senol M., Neirameh A., Tasbozan O., Eslami M., Mirzazadeh M., (2019) Two effective approaches for solving fractional generalized Hirota-Satsuma coupled KdV system arising in interaction of long waves, J Ocean Eng Sci, 4(1), 24-32.
• [8] Podlubny I.., (1998) Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Elsevier, California.
• [9] Gao F., Chi C., (2020) Improvement on conformable fractional derivative and its applications in fractional differential equations, J Funct Spaces, 2020, https://doi.org/10.1155/2020/5852414.
• [10] Debnath L., (2003) Recent applications of fractional calculus to science and engineering, International J Math Math Sci, 2003(54), 3413-3442.
• [11] Khalil R., Al Horani M., Yousef A., Sababheh M., (2014) A new definition of fractional derivative, J Comput Appl Math , 264, 65-70.
• [12] Abdeljawad T., (2015) On conformable fractional calculus, J Comput Appl Math , 279, 57-66.
• [13] Heaviside O., (1899). Electromagnetic Theory, Chelsea Publishing Company, New York.
• [14] Kumar S., (2014). A new analytical modelling for fractional telegraph equation via Laplace transform, Appl Math Model, 38(13), 3154-3163.
• [15] Yıldırım A., (2010). He's homotopy perturbation method for solving the space-and time-fractional telegraph equations, Int J Comput Math, 87(13), 2998-3006.
• [16] Dehghan M., Yousefi S. A., Lotfi A., (2011). The use of He's variational iteration method for solving the telegraph and fractional telegraph equations, Int J Numer Method Biomed Eng, 27(2), 219-231.
• [17] Keskin Y., Oturanc G., (2009). Reduced differential transform method for partial differential equations, Int J Nonlinear Sci Numer Simul, 10(6), 741-750.
• [18] Keskin Y., Oturanc G., (2010) Reduced differential transform method for generalized KdV equations, Math Comput Appl, 15(3), 382-393.
• [19] Acan O., Firat O., Keskin, Y., (2020). Conformable variational iteration method, conformable fractional reduced differential transform method and conformable homotopy analysis method for non-linear fractional partial differential equations, Waves Random Complex Media, 30(2), 250-268.
• [20] Ünal E., Gökdoğan A. (2017) Solution of conformable fractional ordinary differential equations via differential transform method, Optik, 128, 264-273.
• [21] Yavuz M., (2018) Novel solution methods for initial boundary value problems of fractional order with conformable differentiation, Int J Optim Control Theor Appl, 8(1), 1-7.
• [22] Gözütok N.Y., Gözütok U., (2017) Multivariable conformable fractional calculus, arXiv preprint arXiv:1701.00616. [23] Mittag-Leffler G. M., (1903) Sur la nouvelle fonction, CR Acad Sci Paris, 137, 554–558.
• [24] Shrinath M., Bhadane A., (2019) New conformable fractional ELZAKI transformation: Theory and applications, Malaya J Mat , 1, 619-625.
• [25] Veeresha P., Prakasha D. G., (2018) Numerical solution for fractional model of telegraph equation by using q-HATM, arXiv preprint arXiv:1805.03968.
• [26] Khan H., Tunç C., Khan R. A., Shirzoi, A. G., Khan, A., (2018). Approximate Analytical Solutions of Space-Fractional Telegraph Equations by Sumudu Adomian Decomposition Method, Appl Appl Math, 13(2), 12.
• [27] Pandey R. K., Mishra H. K., (2017). Numerical simulation for solution of space–time fractional telegraphs equations with local fractional derivatives via HAFSTM, New Astron, 57, 82-93.