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2018 | 113 | 49-56
Article title

Analytical Solution to Linear Conformable Fractional Partial Differential Equations

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EN
Abstracts
EN
An analytical solution is better than an approximate or series solution of a problem. Here we develop an analytical formulation to solve linear fractional order partial differential equations with given boundary conditions. We discuss the method for the simultaneous fractional derivative, in space as well as time and up to order two. Examples reflect the effectiveness and simplicity of the method. First we convert the fractional derivative into integer order derivative and then use method of separation of variables in usual sense to get the complete solution. The fractional derivative has been taken in the sense of Katugampola’s derivative.
Year
Volume
113
Pages
49-56
Physical description
Contributors
author
  • Department of Applied Science, KIET Group of Institutions, Ghaziabad - 201206, India
author
  • Department of Mathematics, School of Vocational Studies and Applied Sciences, Gautam Buddha University, Gr. Noida - 201310, India
References
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  • [2] I. Podlubny. Fractional Differential equations. Academic Press USA, 1999.
  • [3] Kilbas, H. Srivastava, J. Trujillo, Theory and Applications of Fractional Differential Equations in Math Studies. North-Holland, New York, 2006.
  • [4] R. Khalil, M. Al Horani, A. Yusuf and M. Sababhed. A New Definition of Fractional Derivative. Journal of Computational Applications Math. 264 (2014).
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  • [7] R. Khalil, M. Abu-Hammad, Legendre Fractional Differential Equation and Legendre Fractional Polynomials. International Journal of Applied Mathematical Research 3(3) (2014) 214-219.
  • [8] Udita N. Katugampola, A New Fractional Derivative with Classical Properties. Journal of The American Mathematical Society. arXiv:1410.6535v2 [math.CA] 8 Nov 2014.
  • [9] T. Abdeljawad, On Conformable Fractional Calculus. Journal of Computational and Applied Mathematics 279 (2015) 57-66.
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  • [11] O. S Iyiola, E.R Nwaeze, Some new results on the conformable fractional calculus with application using D’ alembert’s approach. Progr. Frac. Diff. Appl. 2(2) (2016) 115-122
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  • [13] Yucel Cenesiz, Alikurt. The Solution of Time Fractional Heat Equation With New Fractional Derivative Definition. Recent Advances in Applied Mathematic Modelling and Simulation (2015) 195-198
  • [14] D. R. Anderson, D. J. Ulness, Properties of the Katugampola fractional derivative with potential application in quantum mechanics. J. Mathematical Physics 6 (2015).
  • [15] R. Hilfer. Application of fractional Calculus in Physics. World Scientific Publishing Company, Singapore (2000). ISBN 9810234570.
Document Type
article
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bwmeta1.element.psjd-cb260c82-15e4-48f2-8dae-6829953f0a5d
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