Araştırma Makalesi

Series Form Solution to Two Dimensional Heat Equation of Fractional Order

Cilt: 2 Sayı: 4 25 Aralık 2019
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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

Kaynakça

  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.

Ayrıntılar

Birincil Dil

İngilizce

Konular

Matematik

Bölüm

Araştırma Makalesi

Yazarlar

Atta Ullah
Türkiye

Kamal Shah
Türkiye

Yayımlanma Tarihi

25 Aralık 2019

Gönderilme Tarihi

30 Ekim 2019

Kabul Tarihi

27 Aralık 2019

Yayımlandığı Sayı

Yıl 2019 Cilt: 2 Sayı: 4

Kaynak Göster

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, ve 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 (01 Aralık 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, ve R. A. Khan, “Series Form Solution to Two Dimensional Heat Equation of Fractional Order”, RNA, c. 2, sy 4, ss. 193–199, Ara. 2019, [çevrimiçi]. Erişim adresi: 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 (01 Aralık 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, vd. “Series Form Solution to Two Dimensional Heat Equation of Fractional Order”. Results in Nonlinear Analysis, c. 2, sy 4, Aralık 2019, ss. 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]. 01 Aralık 2019;2(4):193-9. Erişim adresi: https://izlik.org/JA75MP53GB