TY  - JOUR
T1  - Numerical Solutions of Conformable Time-Fractional Swift-Hohenberg Equation with Proportional Delay by the Novel Methods
TT  - Oransal Gecikmeli Uyumlu Zaman-Kesirli Swift-Hohenberg Denkleminin Yeni Yöntemlerle Sayısal Çözümleri
AU  - Anaç, Halil
AU  - Erol, Ahmet Semih
AU  - Olgun, Ali
PY  - 2023
DA  - June
DO  - 10.55213/kmujens.1221889
JF  - Karamanoğlu Mehmetbey Üniversitesi Mühendislik ve Doğa Bilimleri Dergisi
JO  - KMUJENS
PB  - Karamanoğlu Mehmetbey Üniversitesi
WT  - DergiPark
SN  - 2687-5071
SP  - 1
EP  - 24
VL  - 5
IS  - 1
LA  - en
AB  - The conformable fractional q-Shehu homotopy analysis transform method and the conformable Shehu transform decomposition method are used to analyze the conformable time-fractional Swift-Hohenberg equations with proportional delay. The graphs of the numerical solutions to this problem are drawn. The proposed methods are effective and consistent, according to numerical simulations.
KW  - Conformable time-fractional Swift-Hohenberg equation
KW  - conformable fractional q-Shehu homotopy analysis transform method
KW  - conformable fractional Shehu transform decomposition method
N2  - Uyumlu kesirli q-Shehu homotopi analizi dönüşüm yöntemi ve uyumlu Shehu dönüşümü ayrıştırma yöntemi, oransal gecikmeli uyumlu zaman-kesirli Swift-Hohenberg denklemlerini analiz etmek için kullanılmıştır. Bu problemin sayısal çözümlerinin grafikleri çizdirilmiştir. Önerilen yöntemler, sayısal simülasyonlara göre etkili ve tutarlıdır.
CR  - Abdeljawad T., On conformable fractional calculus, Journal of Computational and Applied Mathematics, Vol. 279, pp. 57-66, (2015).
CR  - Baleanu D., Diethelm K., Scalas E., Trujillo JJ., Fractional Calculus: Models and Numerical Methods, Boston, MA, USA, World Scientific, (2012).
CR  - Baleanu D., Wu GC., Zeng SD., Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations, Chaos Solitons Fractals, Vol. 102, pp. 99–105, (2017).
CR  - Benattia ME., Belghaba K., Shehu conformable fractional transform, theories and applications, Cankaya University Journal of Science and Engineering, Vol. 18, No. 1, pp. 24-32, (2021).
CR  - Caponetto R., Dongola G., Fortuna L., Gallo A., New results on the synthesis of FO-PID controllers, Communications in Nonlinear Science and Numerical Simulation, Vol. 15, pp. 997–1007, (2010).
CR  - Caputo M., Elasticità e Dissipazione, Bologna, Italy, Zanichelli, (1969).
CR  - Chen X., Wang L., The variational iteration method for solving a neutral functional-differential equation with proportional delays, Computers and Mathematics with Applications, Vol. 59, No. 8, pp. 2696-2702, (2010).
CR  - Cross MC., Hohenberg PC., Pattern formation outside of equilibrium, Reviews of modern physics, Vol. 65, No. 3, pp. 851, (1993).
CR  - Debnath L., Recent applications of fractional calculus to science and engineering, International Journal of Mathematics and Mathematical Sciences, Vol. 2003, No. 54, pp. 3413-3442, (2003).
CR  - Esen A., Sulaiman TA., Bulut H., Baskonus HM., Optical solitons to the space-time fractional (1+1)-dimensional coupled nonlinear Schrödinger equation, Optik, Vol. 167, pp. 150–156, (2018).
CR  - Gao F., Chi C., Improvement on conformable fractional derivative and its applications in fractional differential equations, Journal of Function Spaces, 2020, 5852414, (2020).
CR  - Gözütok NY., Gözütok U., Multivariable conformable fractional calculus, Filomat, Vol. 32, No. 1, pp. 45-53, (2017).
CR  - Hohenberg PC., Swift JB., Effects of additive noise at the onset of Rayleigh-Bénard convection, Physical Review A, Vol. 46, No. 8, pp. 4773, (1992).
CR  - Hoyle RB., Pattern Formation, Cambridge, UK, Cambridge University Press, (2006).
CR  - Keller AA., Contribution of the delay differential equations to the complex economic macrodynamics, WSEAS Transactions on Systems, Vol. 9, No. 4, pp. 358–371, (2010).
CR  - Khalil R., Al Horani M., Yousef A., Sababheh M., A new definition of fractional derivative, Journal of Computational and Applied Mathematics, Vol. 264, pp. 65-70, (2014).
CR  - Khan NA., Khan NU., Ayaz M., Mahmood A., Analytical methods for solving the time-fractional Swift–Hohenberg (S–H) equation, Comput. Math. Appl. Vol. 2011, No 61, pp. 2181–2185, (2011).
CR  - Khan  A., Liaqat MI., Alqudah MA., Abdeljawad T., Analysis of the Conformable Temporal-Fractional Swift-Hohenberg Equation Using a Novel Computational Technique, Fractals, (2023).
CR  - Kilbas AA., Srivastava HM., Trujillo JJ, Theory and applications of fractional differential equations, Amsterdam, The Netherlands, Elsevier B.V., (2006).
CR  - Lega J., Moloney JV., Newell AC., Swift-Hohenberg equation for lasers, Physical review letters, Vol. 73, No. 22, pp. 2978, (1994).
CR  - Liaqat MI., Okyere E., The Fractional Series Solutions for the Conformable Time-Fractional Swift-Hohenberg Equation through the Conformable Shehu Daftardar-Jafari Approach with Comparative Analysis, Journal of Mathematics, 2022, Article ID 3295076, 20 pages, (2022).
CR  - Liouville J., Mémoire sur quelques questions de géométrie et de mécanique, et sur un nouveau genre de calcul pour résoudre ces questions, Ecole polytechnique, Vol. 13, pp. 71-162, (1832).
CR  - Liu DY., Gibaru O., Perruquetti W., Laleg-Kirati TM., Fractional order differentiation by integration and error analysis in noisy environment, IEEE Transactions on Automatic Control, Vol. 60, pp. 2945–2960, (2015).
CR  - Merdan M., A numeric–analytic method for time-fractional Swift–Hohenberg (S-H) equation with modified Riemann–Liouville derivative, Appl. Math. Model. Vol. 2013, No. 37, pp. 4224–4231, (2013).
CR  - Miller KS, Ross B., An Introduction to Fractional Calculus and Fractional Differential Equations, New York, NY, USA, Wiley, (1993).
CR  - Mittag-Leffler GM., Sur la nouvelle fonction E_α (x), Comptes Rendus de l’Academie des Sciences, Vol. 137, pp. 554-558, (1903).
CR  - Omorodion SS., Conformable fractional reduced differential transform method for solving linear and nonlinear time-fractional Swift-Hohenberg (SH) equation, International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol. 8, No. 6, pp. 20-29, (2021).
CR  - Peletier LA., Rottschäfer V., Large time behaviour of solutions of the Swift–Hohenberg equation, Comptes Rendus Mathematique, Vol. 336, No. 3, pp. 225-230, (2003).
CR  - Podlubny I., Fractional Differential Equations, New York, NY, USA, Academic Press, (1999).
CR  - Pomeau Y., Zaleski S., Manneville P., Dislocation motion in cellular structures, Physical Review A, Vol. 27, No. 5, pp. 2710, (1983).
CR  - Povstenko Y., Linear Fractional Diffusion-Wave Equation for Scientists and Engineers, New York, NY, USA, Birkhäuser, (2015).
CR  - Prakash A., Veeresha P., Prakasha DG., Goyal M., A homotopy technique for fractional order multi-dimensional telegraph equation via Laplace transform, The European Physical Journal Plus, Vol. 134, pp. 1–18, (2019).
CR  - Prakasha DG., Veeresha P., Baskonus HM., Residual power series method for fractional Swift–Hohenberg equation, Fractal and Fractional, Vol. 3, No. 1, pp. 9, (2019).
CR  - Riemann GFB, Versuch einer allgemeinen Auffassung der Integration und Differentiation, Leipzig, Germany, Gesammelte Mathematische Werke, (1896).
CR  - Singh BK., Kumar P., Fractional variational iteration method for solving fractional partial differential equations with proportional delay, International Journal of Differential. Equations, 5206380, (2017).
CR  - Sweilam NH., Hasan MMA., Baleanu D., New studies for general fractional financial models of awareness and trial advertising decisions, Chaos Solitons Fractals, Vol. 104, pp. 772–784, (2017).
CR  - Swift J., Hohenberg PC., Hydrodynamic fluctuations at the convective instability, Physical Review A, Vol. 15, No. 1, pp. 319, (1977).
CR  - Veeresha P., Prakasha DG., Baskonus HM., New numerical surfaces to the mathematical model of cancerchemotherapy effect in Caputo fractional derivatives, Chaos, 29, 013119, (2019).
CR  - Veeresha P., Prakasha DG., Baskonus HM., Novel simulations to the time-fractional Fisher’s equation, Mathematical Sciences, Vol. 13, No. 1, pp.33-42, (2019).
CR  - Veeresha P., Prakasha DG., Baleanu D., Analysis of fractional Swift‐Hohenberg equation using a novel computational technique, Mathematical Methods in the Applied Sciences, Vol. 43, No. 4, pp. 1970-1987, (2020).
CR  - Vishal K., Kumar S., Das S., Application of homotopy analysis method for fractional Swift-Hohenberg equation revisited, Appl. Math. Model. Vol. 2012, No. 36, pp. 3630–3637, (2012).
CR  - Vishal K., Das S., Ong SH., Ghosh P., On the solutions of fractional Swift-Hohenberg equation with dispersion, Appl. Math. Comput. Vol. 2013, No. 219, pp. 5792–5801, (2013).
CR  - Wu J., Theory and Applications of Partial Functional Differential Equations, New York, NY, USA, Springer, (1996).
UR  - https://doi.org/10.55213/kmujens.1221889
L1  - https://dergipark.org.tr/tr/download/article-file/2843290
ER  -