Solution of linear and non-linear partial differential equation of fractional order
Keywords:α-fractional derivative and integral, Fractional linear and nonlinear partial differential equation, Method of separation of variables
We know that the solution of partial differential equations by analytical method is better than the solution by approximate or series solution method. In this paper, we discuss the solution of linear and non-linear fractional partial differential equations involving derivatives with respect to time or space variables by converting them into the partial differential equations of integer order. Also we develop an analytical formulation to solve such fractional partial differential equations. Moreover, we discuss the method to solve the fractional partial differential equations in space as well as time variables simultaneously with the help of some examples.
T. Abdeljawad, “On Conformable Fractional Calculus”, Journal of Computational and Applied Mathematics, vol. 279, pp. 57-66, 2015.
R. Almeida, M. Guzowska, and T. Odzijewicz, “A Remark on Local Fractional Calculus and Ordinary Derivatives”, 2017, arXiv:1612.00214
D. R. Anderson and D. J. Ulness, “Properties of the Katugampola fractional derivative with potential application in quantum mechanics”, Journal of Mathematical Physics , vol. 56, no. 6, 2015.
H. Batarfi, J. Losada, J. J. Nieto, and W. Shammakh, “ThreePoint Boundary Value Problems for Conformable Fractional Differential Equations”, Journal of Functional Space, vol. 2015, Art. ID. 706383, 2015, https://doi.org/10.1155/2015/706383
O. S Iyiola and E.R Nwaeze, “Some new results on the conformable fractional calculus with application using D Alembert approach”, Progress in Fractional Differentiation and Applications, vol. 2, no. 2, pp. 115-122, 2016.
Udita N. Katugampola, “A New Fractional Derivative with Classical Properties”, 2014, arXiv:1410.6535v2
R. Khalil, M. Al Horani, A. Yusuf, and M. Sababhed, “A New Definition of Fractional Derivative”, Journal of Computational and Applied Mathematics, vol. 264, pp. 65-70, 2014.
R. Khalil, and M. Abu-Hammad, “Conformable Fractional Heat Differential Equation”, International Journal of Pure and Applied Mathematics, vol. 94, pp. 215-217, 2014.
R. Khalil and M. Abu-Hammad, “Abel’s Formula and Wronskian for Conformable Fractional Differential Equations”, International Journal of Differential Equations and Applications, vol. 13, pp. 177-183, 2014.
R. Khalil and M. Abu-Hammad, “Legendre Fractional Differential Equation and Legendre Fractional Polynomials”, International Journal of Applied Mathematical Research, vol. 3, no. 3, pp. 214-219, 2014.
R. Khalil and M. Abu-Hammad, “Fractional Fourier Series with Applications”, American Journal of Computational and Applied Mathematics, vol. 4, no. 6, pp. 187-191, 2014.
A. Kilbas, H. Srivastava and J. Trujillo, Theory and Applications of Fractional Differential Equations in Math Studies. New York: North-Holland, 2006.
R. Hilfer, Application of fractional Calculus in Physics. Singapore: World Scientific Publishing Company, 2000.
K. S. Millar, An Introduction to Fractional Calculus and Fractional Differential Equations. New York: J Wiley and Sons, 1993.
I. Podlubny, Fractional Differential equations. San Diego: Academic Press, 1999.
R. A. Muneshwar, K. L. Bondar, and Y. H. Shirole, “Some Properties of α Fractional Derivative and It’s Applications”, Journal of Taylor Francis (Communicated).
Y. Cenesiz and A. Kurt, “The Solution of Time Fractional Heat Equation With New Fractional Derivative Definition,” in Recent advances in applied mathematics, modelling and simulation: proceedings of the 8th International Conference on Applied Mathematics, Simulation, Modelling (ASM '14), Florence, Italy, November 22-24, 2014, pp. 195–198.
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Copyright (c) 2021 Raju Muneshwar, K. L. Bondar, Y. H. Shirole
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