Approximate Solutions of the Time-Fractional Kadomtsev-Petviashvili Equation with Conformable Derivative
Yıl: 2019 Cilt: 12 Sayı: 2 Sayfa Aralığı: 796 - 806 Metin Dili: İngilizce DOI: 10.18185/erzifbed.488471 İndeks Tarihi: 20-12-2020
Approximate Solutions of the Time-Fractional Kadomtsev-Petviashvili Equation with Conformable Derivative
Öz: In this study, residual power series method, namely RPSM, is applied to solve time-fractional KadomtsevPetviashvili (K-P) differential equation. In the solution procedure, the fractional derivatives are explained in theconformable sense. The model is solved approximately and the obtained results are compared with exactsolutions obtained by the sub-equation method. The results reveal that the present method is accurate,dependable, simple to apply and a good alternative for seeking solutions of nonlinear fractional partialdifferential equations
Anahtar Kelime: Zaman-Kesirli Kadomtsev- Petviashvili Denkleminin Conformable Türev ile Yaklaşık Çözümleri
Öz: Bu çalışmada, zaman-kesirli Kadomtsev-Petviashvili (K-P) diferansiyel denklemini çözmek için Rezidual Kuvvet Serisi Metodu (RPSM) kullanılmıştır. Çözüm prosedüründe, kesirli türevler, conformable kesirli türev tanımına göre hesaplanmıştır. Bu model yaklaşık olarak çözülmüş ve elde edilen sonuçlar, sub-equation metodu ile elde edilen tam çözümlerle karşılaştırılmıştır. Sonuçlar, mevcut yöntemin doğru, güvenilir, uygulanmasının basit olduğunu ve doğrusal olmayan kısmi diferansiyel denklemlerin çözümü için iyi bir alternatif olduğunu ortaya koymaktadır
Anahtar Kelime: Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
- Abdeljawad, T. (2015). On conformable fractional calculus. Journal of computational and Applied Mathematics, 279, 57-66.
- Ahmad, R. S. (2015). An analytical solution of the fractional Navier-Stokes equation by residual power series method, Doctoral dissertation, Zarqa University.
- Alabsi T. Y. (2017). Solution of Conformable Fractional Navier-Stokes Equation, M.S. thesis, Zarqa University.
- Alquran, M. (2014). Analytical solutions of fractional foam drainage equation by residual power series method. Mathematical sciences, 8(4), 153-160.
- Alquran, M. (2015). Analytical solution of time-fractional two-component evolutionary system of order 2 by residual power series method. J. Appl. Anal. Comput, 5(4), 589- 599.
- Arikoglu, A., & Ozkol, I. (2009). Solution of fractional integro-differential equations by using fractional differential transform method. Chaos, Solitons & Fractals, 40(2), 521-529.
- Arqub, O. A. (2013). Series solution of fuzzy differential equations under strongly generalized differentiability. Journal of Advanced Research in Applied Mathematics, 5(1), 31-52.
- Arqub, O. A., El-Ajou, A., Bataineh, A. S., & Hashim, I. (2013). A representation of the exact solution of generalized Lane-Emden equations using a new analytical method. In Abstract and Applied Analysis (Vol. 2013). Hindawi.
- Atangana, A., Baleanu, D., & Alsaedi, A. (2015). New properties of conformable derivative. Open Mathematics, 13(1).
- Caputo, M. (1967). Linear models of dissipation whose Q is almost frequency independent-II. Geophysical Journal International, 13(5), 529-539.
- Carpinteri, A., & Mainardi, F. (Eds.). (2014). Fractals and fractional calculus in continuum mechanics (Vol. 378). Springer. Das, S. (2011). Functional fractional calculus. Springer Science & Business Media.
- Diethelm, K. (2010). The analysis of fractional differential equations: An application-oriented exposition using differential operators of Caputo type. Springer Science & Business Media.
- Durur, H., Taşbozan, O., Kurt, A., & Şenol, M. (2019) New Wave Solutions of Time Fractional Kadomtsev-Petviashvili Equation Arising In the Evolution of Nonlinear Long Waves of Small Amplitude. Submitted.
- El-Ajou, A., Arqub, O. A., Zhour, Z. A., & Momani, S. (2013). New results on fractional power series: theories and applications. Entropy, 15(12), 5305-5323.
- El-Sayed, A. M. A., Nour, H. M., Raslan, W. E., & El-Shazly, E. S. (2015). A study of projectile motion in a quadratic resistant medium via fractional differential transform method. Applied Mathematical Modelling, 39(10-11), 2829-2835.
- Ghazanfari, B., & Veisi, F. (2011). Homotopy analysis method for the fractional nonlinear equations. Journal of King Saud UniversityScience, 23(4), 389-393.
- Guo, S., & Mei, L. (2011). The fractional variational iteration method using He's polynomials. Physics Letters A, 375(3), 309- 313.
- Heaviside, O. (2008). Electromagnetic theory (Vol. 3). Cosimo, Inc.
- Jafari, H., & Daftardar-Gejji, V. (2006). Solving linear and nonlinear fractional diffusion and wave equations by Adomian decomposition. Applied Mathematics and Computation, 180(2), 488-497.
- Jaradat, H. M., Al-Shara, S., Khan, Q. J., Alquran, M., & Al-Khaled, K. (2016). Analytical solution of time-fractional Drinfeld-Sokolov-Wilson system using residual power series method. IAENG Int. J. Appl. Math, 46(1), 64-70.
- Kadomtsev, B. B., & Petviashvili, V. I. (1970, December). On the stability of solitary waves in weakly dispersing media. In Sov. Phys. Dokl (Vol. 15, No. 6, pp. 539-541).
- Kaya, D., & El-Sayed, S. M. (2003). Numerical soliton-like solutions of the potential Kadomtsev–Petviashvili equation by the decomposition method. Physics Letters A, 320(2-3), 192-199.
- Khalil, R., Al Horani, M., Yousef, A., & Sababheh, M. (2014). A new definition of fractional derivative. Journal of Computational and Applied Mathematics, 264, 65-70.
- Kumar, A., Kumar, S., & Singh, M. (2016). Residual power series method for fractional Sharma-Tasso-Olever equation. Communications in Numerical Analysis, 2016(1), 1-10.
- Momani, S., & Shawagfeh, N. (2006). Decomposition method for solving fractional Riccati differential equations. Applied Mathematics and Computation, 182(2), 1083- 1092.
- Momani, S., Odibat, Z., & Erturk, V. S. (2007). Generalized differential transform method for solving a space-and timefractional diffusion-wave equation. Physics Letters A, 370(5-6), 379-387.
- Oldham, K. B. (2010). Fractional differential equations in electrochemistry. Advances in Engineering Software, 41(1), 9-12.
- Podlubny, I. (1999). Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Mathematics in science and engineering, 198, 261-300.
- Song, L., & Zhang, H. (2007). Application of homotopy analysis method to fractional KdV– Burgers–Kuramoto equation. Physics Letters A, 367(1-2), 88-94.
- Song, L., & Wang, W. (2013). A new improved Adomian decomposition method and its application to fractional differential equations. Applied Mathematical Modelling, 37(3), 1590-1598.
- Tasbozan, O., Çenesiz, Y., & Kurt, A. (2016). New solutions for conformable fractional Boussinesq and combined KdV-mKdV equations using Jacobi elliptic function expansion method. The European Physical Journal Plus, 131(7), 244.
- Şenol, M., & Dolapci, I. T. (2016). On the Perturbation–Iteration Algorithm for fractional differential equations. Journal of King Saud University-Science, 28(1), 69-74.
- Şenol, M., Alquran, M., & Kasmaei, H. D. (2018). On the comparison of perturbationiteration algorithm and residual power series method to solve fractional ZakharovKuznetsov equation. Results in Physics, 9, 321-327.
- Wu, G. C., & Lee, E. W. M. (2010). Fractional variational iteration method and its application. Physics Letters A, 374(25), 2506- 2509.
- Yakar, A., & Koksal, M. E. (2012). Existence results for solutions of nonlinear fractional differential equations. Abstract and Applied Analysis (Vol. 2012). Hindawi.
- Yeroglu, C., & Senol, B. (2013). Investigation of robust stability of fractional order multilinear affine systems: 2q-convex parpolygon approach. Systems & Control Letters, 62(10), 845-855.
- Zhaosheng, Y., & Jianzhong, L. (1998). Numerical research on the coherent structure in the viscoelastic second-order mixing layers. Applied Mathematics and Mechanics, 19(8), 717-723.
| APA | DURUR H, ŞENOL M, Kurt A, TAŞBOZAN O (2019). Approximate Solutions of the Time-Fractional Kadomtsev-Petviashvili Equation with Conformable Derivative. , 796 - 806. 10.18185/erzifbed.488471 |
| Chicago | DURUR Hülya,ŞENOL Mehmet Selçuk,Kurt Ali,TAŞBOZAN Orkun Approximate Solutions of the Time-Fractional Kadomtsev-Petviashvili Equation with Conformable Derivative. (2019): 796 - 806. 10.18185/erzifbed.488471 |
| MLA | DURUR Hülya,ŞENOL Mehmet Selçuk,Kurt Ali,TAŞBOZAN Orkun Approximate Solutions of the Time-Fractional Kadomtsev-Petviashvili Equation with Conformable Derivative. , 2019, ss.796 - 806. 10.18185/erzifbed.488471 |
| AMA | DURUR H,ŞENOL M,Kurt A,TAŞBOZAN O Approximate Solutions of the Time-Fractional Kadomtsev-Petviashvili Equation with Conformable Derivative. . 2019; 796 - 806. 10.18185/erzifbed.488471 |
| Vancouver | DURUR H,ŞENOL M,Kurt A,TAŞBOZAN O Approximate Solutions of the Time-Fractional Kadomtsev-Petviashvili Equation with Conformable Derivative. . 2019; 796 - 806. 10.18185/erzifbed.488471 |
| IEEE | DURUR H,ŞENOL M,Kurt A,TAŞBOZAN O "Approximate Solutions of the Time-Fractional Kadomtsev-Petviashvili Equation with Conformable Derivative." , ss.796 - 806, 2019. 10.18185/erzifbed.488471 |
| ISNAD | DURUR, Hülya vd. "Approximate Solutions of the Time-Fractional Kadomtsev-Petviashvili Equation with Conformable Derivative". (2019), 796-806. https://doi.org/10.18185/erzifbed.488471 |
| APA | DURUR H, ŞENOL M, Kurt A, TAŞBOZAN O (2019). Approximate Solutions of the Time-Fractional Kadomtsev-Petviashvili Equation with Conformable Derivative. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 12(2), 796 - 806. 10.18185/erzifbed.488471 |
| Chicago | DURUR Hülya,ŞENOL Mehmet Selçuk,Kurt Ali,TAŞBOZAN Orkun Approximate Solutions of the Time-Fractional Kadomtsev-Petviashvili Equation with Conformable Derivative. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi 12, no.2 (2019): 796 - 806. 10.18185/erzifbed.488471 |
| MLA | DURUR Hülya,ŞENOL Mehmet Selçuk,Kurt Ali,TAŞBOZAN Orkun Approximate Solutions of the Time-Fractional Kadomtsev-Petviashvili Equation with Conformable Derivative. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol.12, no.2, 2019, ss.796 - 806. 10.18185/erzifbed.488471 |
| AMA | DURUR H,ŞENOL M,Kurt A,TAŞBOZAN O Approximate Solutions of the Time-Fractional Kadomtsev-Petviashvili Equation with Conformable Derivative. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi. 2019; 12(2): 796 - 806. 10.18185/erzifbed.488471 |
| Vancouver | DURUR H,ŞENOL M,Kurt A,TAŞBOZAN O Approximate Solutions of the Time-Fractional Kadomtsev-Petviashvili Equation with Conformable Derivative. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi. 2019; 12(2): 796 - 806. 10.18185/erzifbed.488471 |
| IEEE | DURUR H,ŞENOL M,Kurt A,TAŞBOZAN O "Approximate Solutions of the Time-Fractional Kadomtsev-Petviashvili Equation with Conformable Derivative." Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 12, ss.796 - 806, 2019. 10.18185/erzifbed.488471 |
| ISNAD | DURUR, Hülya vd. "Approximate Solutions of the Time-Fractional Kadomtsev-Petviashvili Equation with Conformable Derivative". Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi 12/2 (2019), 796-806. https://doi.org/10.18185/erzifbed.488471 |
