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
Kaynakça
- [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] R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
- [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] 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] V. Lakshmikantham, S. Leela and J. Vasundhara, Theory of Fractional Dynamic Systems, Cambridge Academic Publishers, Cambridge, UK, 2009.
- [6] V. Lakshmikantham and S. Leela, Naguma-type uniqueness result for fractional differential equations, Non- linear Anal., 71 (2009) 2886--2889.
- [7] K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.
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Ayrıntılar
Birincil Dil
İngilizce
Konular
Matematik
Bölüm
Araştırma Makalesi
Yayımlanma Tarihi
25 Aralık 2019
Gönderilme Tarihi
30 Ekim 2019
Kabul Tarihi
27 Aralık 2019
Yayımlandığı Sayı
Yıl 2019 Cilt: 2 Sayı: 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, 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