Research Article

Series Form Solution to Two Dimensional Heat Equation of Fractional Order

Volume: 2 Number: 4 December 25, 2019
EN

Series Form Solution to Two Dimensional Heat Equation of Fractional Order

Abstract

In this article we develop series type solution to two dimensional wave equation involving external source term of fractional order. For the require result, we use iterative Laplace transform. The solution is computed in series form which is rapidly convergent to exact value. Some examples are given to illustrate the establish results.

Keywords

References

  1. [1] H. Eltayeb, Hassan, and A. Kiliçman, A note on solutions of wave, Laplace's and heat equations with convolution terms by using a double Laplace transform, Applied Mathematics Letters 21(12) (2008) 1324- 1329.
  2. [2] R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
  3. [3] T. Khan, K. Shah, R.A. Khan and A. Khan, Solution of fractional order heat equation via triple Laplace transform in 2 dimensions, Mathematical Methods in the Applied Sciences 41(2) (2018): 818-825.
  4. [4] A.A. Kilbas, H. Srivastava and J. Trujillo, Theory and application of fractional differential equations, North Holland Mathematics Studies, vol. 204, Elseveir, Amsterdam, 2006.
  5. [5] V. Lakshmikantham, S. Leela and J. Vasundhara, Theory of Fractional Dynamic Systems, Cambridge Academic Publishers, Cambridge, UK, 2009.
  6. [6] V. Lakshmikantham and S. Leela, Naguma-type uniqueness result for fractional differential equations, Non- linear Anal., 71 (2009) 2886--2889.
  7. [7] K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.
  8. [8] I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, Academic Press, New York, 1999.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Atta Ullah
Türkiye

Kamal Shah
Türkiye

Publication Date

December 25, 2019

Submission Date

October 30, 2019

Acceptance Date

December 27, 2019

Published in Issue

Year 2019 Volume: 2 Number: 4

APA
Ullah, A., Shah, K., & Khan, R. A. (2019). Series Form Solution to Two Dimensional Heat Equation of Fractional Order. Results in Nonlinear Analysis, 2(4), 193-199. https://izlik.org/JA75MP53GB
AMA
1.Ullah A, Shah K, Khan RA. Series Form Solution to Two Dimensional Heat Equation of Fractional Order. RNA. 2019;2(4):193-199. https://izlik.org/JA75MP53GB
Chicago
Ullah, Atta, Kamal Shah, and Rahmat Ali Khan. 2019. “Series Form Solution to Two Dimensional Heat Equation of Fractional Order”. Results in Nonlinear Analysis 2 (4): 193-99. https://izlik.org/JA75MP53GB.
EndNote
Ullah A, Shah K, Khan RA (December 1, 2019) Series Form Solution to Two Dimensional Heat Equation of Fractional Order. Results in Nonlinear Analysis 2 4 193–199.
IEEE
[1]A. Ullah, K. Shah, and R. A. Khan, “Series Form Solution to Two Dimensional Heat Equation of Fractional Order”, RNA, vol. 2, no. 4, pp. 193–199, Dec. 2019, [Online]. Available: https://izlik.org/JA75MP53GB
ISNAD
Ullah, Atta - Shah, Kamal - Khan, Rahmat Ali. “Series Form Solution to Two Dimensional Heat Equation of Fractional Order”. Results in Nonlinear Analysis 2/4 (December 1, 2019): 193-199. https://izlik.org/JA75MP53GB.
JAMA
1.Ullah A, Shah K, Khan RA. Series Form Solution to Two Dimensional Heat Equation of Fractional Order. RNA. 2019;2:193–199.
MLA
Ullah, Atta, et al. “Series Form Solution to Two Dimensional Heat Equation of Fractional Order”. Results in Nonlinear Analysis, vol. 2, no. 4, Dec. 2019, pp. 193-9, https://izlik.org/JA75MP53GB.
Vancouver
1.Atta Ullah, Kamal Shah, Rahmat Ali Khan. Series Form Solution to Two Dimensional Heat Equation of Fractional Order. RNA [Internet]. 2019 Dec. 1;2(4):193-9. Available from: https://izlik.org/JA75MP53GB