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Saglam Ozkan, Yeşim, Yasar, Emrullah. (1402). Prolific new M-fractional soliton behaviors to the Schrödinger type Ivancevic option pricing model by two efficient techniques. سامانه مدیریت نشریات علمی, 12(2), 207-225. doi: 10.22034/cmde.2023.56140.2345
Yeşim Saglam Ozkan; Emrullah Yasar. "Prolific new M-fractional soliton behaviors to the Schrödinger type Ivancevic option pricing model by two efficient techniques". سامانه مدیریت نشریات علمی, 12, 2, 1402, 207-225. doi: 10.22034/cmde.2023.56140.2345
Saglam Ozkan, Yeşim, Yasar, Emrullah. (1402). 'Prolific new M-fractional soliton behaviors to the Schrödinger type Ivancevic option pricing model by two efficient techniques', سامانه مدیریت نشریات علمی, 12(2), pp. 207-225. doi: 10.22034/cmde.2023.56140.2345
Saglam Ozkan, Yeşim, Yasar, Emrullah. Prolific new M-fractional soliton behaviors to the Schrödinger type Ivancevic option pricing model by two efficient techniques. سامانه مدیریت نشریات علمی, 1402; 12(2): 207-225. doi: 10.22034/cmde.2023.56140.2345

Prolific new M-fractional soliton behaviors to the Schrödinger type Ivancevic option pricing model by two efficient techniques

Computational Methods for Differential Equations
مقاله 2، دوره 12، شماره 2، خرداد 2024، صفحه 207-225    اصل مقاله (1.12 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.56140.2345
نویسندگان
Yeşim Saglam Ozkan؛ Emrullah Yasar*
Department of Mathematics, Faculty of Arts and Sciences, Bursa Uludag University, 16059 Bursa, Turkey.
چکیده
The principal purpose of this research is to study the M-fractional nonlinear quantum-probability grounded Schrödinger kind Ivancevic option pricing model (IOPM). This well-known economic model is an alternative of the standard Black-Scholes pricing model which represents a controlled Brownian motion in an adaptive setting with relation to nonlinear Schrödinger equation. The exact solutions of the underlying equation have been derived through the well-organized extended modified auxiliary equation mapping and generalized exponential rational function methods. Different forms of optical wave structures including dark, bright, and singular solitons are derived. To the best of our knowledge, verified solutions using Maple are new. The results obtained will contribute to the enrichment of the existing literature of the model under consideration. Moreover, some sketches are plotted to show more about the dynamic behavior of this model.
کلیدواژه‌ها
The extended modified auxiliary equation mapping method؛ The generalized exponential rational function method؛ Ivancevic option pricing model؛ M-fractional derivative
مراجع
  • [1] S. Z. S. Abdalla and P. Winker, Modelling stock market volatility using univariate GARCH models: Evidence from Sudan and Egypt, International Journal of Economics and Finance, 4(8) (2012), 161-176.
  • [2] M. A. Akbar, A. M. Wazwaz, F. Mahmud, D. Baleanu, R. Roy, H. K. Barman, W. Mahmoud, M. A. Al Sharif, and M. S. Osman, Dynamical behavior of solitons of the perturbed nonlinear Schr¨odinger equation and microtubules through the generalized Kudryashov scheme, Results in Physics, 43 (2022), 106079.
  • [3] G. Akram, M. Sadaf, M. Dawood, M. Abbas, and D. Baleanu, Solitary wave solutions to Gardner equation using improved tan  -expansion method, AIMS Mathematics, 8(2) (2023), 4390-4406.
  • [4] G. Akram and M. Sarfraz, Multiple optical soliton solutions for CGL equation with Kerr law nonlinearity via extended modified auxiliary equation mapping method, Optik, 242 (2021), 167258.
  • [5] K. K. Ali, M. A. Abd El Salam, E. M. Mohamed, B. Samet, S. Kumar, and M.S. Osman, Numerical solution for generalized nonlinear fractional integro-differential equations with linear functional arguments using Chebyshev series, Advances in Difference Equations, 2020(1) (2020), 1-23.
  • [6] A. Biswas, M. Ekici, A. Sonmezoglu, and M. R. Belic, Highly dispersive optical solitons with Kerr law nonlinearity by extended Jacobi’s elliptic function expansion, Optik, 183 (2019), 395-400.
  • [7] F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Polit. Econ. 81 (1973), 637–654.
  • [8] Q. Chen, H. M. Baskonus, W. Gao, and E. Ilhan, Soliton theory and modulation instability analysis: The Ivancevic option pricing model in economy, Alexandria Engineering Journal,61(10) (2022), 7843-7851.
  • [9] Y. Q. Chen, Y. H. Tang, J. Manafian, H. Rezazadeh, and M. S. Osman, Dark wave, rogue wave and perturbation solutions of Ivancevic option pricing model, Nonlinear Dynamics, 105(3) (2021), 2539-2548.
  • [10] M. Contreras, R. Pellicer, M. Villena, and A. Ruiz, A quantum model of option pricing: when Black-Scholes meets Schr¨odinger and its semi-classical limit, Physica A: Statistical Mechanics and Its Applications, 389(23) (2010), 5447– 5459.
  • [11] S. O. Edeki, O. O. Ugbebor, and O. Gonzalez-Gaxiola, Analytical solutions of the Ivancevic option pricing model with a nonzero adaptive market potential, International Journal of Pure and Applied Mathematics, 115(1) (2017), 187-198.
  • [12] S. O. Edeki, O. O. Ugbebor, and J. R. de Ch’avez, Solving the Ivancevic Pricing Model Using the He’s Frecuency Amplitude Formulation, European Journal of Pure and Applied Mathematics, 10(4) (2017), 631-637.
  • [13] A. A. Elmandouh and M. E. Elbrolosy, Integrability, Variational Principle, Bifurcation, and New Wave Solutions for the Ivancevic Option Pricing Model, Journal of Mathematics, (2022), 2022.
  • [14] B. Ghanbari and A. Akgul, Abundant new analytical and approximate solutions to the generalized Schamel equation, Physica Scripta, 95(7) (2020), 075201.
  • [15] B. Ghanbari and D. Baleanu, Applications of two novel techniques in finding optical soliton solutions of modified nonlinear Schrodinger equations, Results in Physics, (2022), 106171.
  • [16] B. Ghanbari, H. Gu¨nerhan, O. A. Ilhan, and H. M. Baskonus,˙ Some new families of exact solutions to a new extension of nonlinear Schr¨odinger equation, Physica Scripta, 95(7) (2020), 075208.
  • [17] B. Ghanbari and J. G. Liu, Exact solitary wave solutions to the (2+ 1)-dimensional generalised Camassa–Holm–Kadomtsev–Petviashvili equation, Pramana, 94(1) (2020), 21.
  • [18] K. Hosseini, K. Sadri, S. Salahshour, D. Baleanu, M. Mirzazadeh, and M. Inc, The generalized Sasa-Satsuma equation and its optical solitons, Optical and Quantum Electronics, 54(11) (2022), 1-15.
  • [19] J. C. Hull, Options, futures, and other derivatives, Pearson, USA, 2006.
  • [20] A. Hussain, A. Jhangeer, M. Abbas, I. Khan, and E. S. M. Sherif, Optical solitons of fractional complex Ginzburg–Landau equation with conformable, beta, and M-truncated derivatives: A comparative study, Advances in Difference Equations, 2020 (2020), 1-19.
  • [21] H. F. Ismael, H. Bulut, C. Park, and M. S. Osman, M-lump, N-soliton solutions, and the collision phenomena for the (2+ 1)-dimensional Date-Jimbo-Kashiwara-Miwa equation, Results in Physics, 19 (2020), 103329.
  • [22] M. S. Iqbal, A. R. Seadawy, M. Z. Baber, and M. Qasim, Application of modified exponential rational function method to Jaulent-Miodek system leading to exact classical solutions, Chaos, Solitons , Fractals, 164 (2022),112600.
  • [23] V. G. Ivancevic, Adaptive-wave alternative for the black-scholes option pricing model, Cognitive Computation, 2(1) (2010), 17-30.
  • [24] R. M. Jena, S. Chakraverty, and D. Baleanu, A novel analytical technique for the solution of time-fractional Ivancevic option pricing model, Phys. A: Stat. Mech. Appl. 550 (2020), 124380.
  • [25] A. Kartono, S. Solekha, and T. Sumaryada, Foreign currency exchange rate prediction using non-linear Schr¨odinger equations with economic fundamental parameters, Chaos, Solitons Fractals, 152 (2021), 111320.
  • [26] A. Kirman and G. Teyssiere, Microeconomic models for long memory in the volatility of financial time series, Studies in Nonlinear Dynamics Econometrics, (4) (2002).
  • [27] B. Kopcasiz and E. Yasar, The investigation of unique optical soliton solutions for dual-mode nonlinear Schr¨odingers equation with new mechanisms. Journal of Optics, (2022), 1-15.
  • [28] S. Kumar, M. Niwas, M. S. Osman, and M. A. Abdou, Abundant different types of exact soliton solution to the (4+ 1)-dimensional Fokas and (2+ 1)-dimensional breaking soliton equations, Communications in Theoretical Physics, 73(10) (2021), 105007.
  • [29] V. Kumar and A. M. Wazwaz, Lie symmetry analysis and soliton solutions for complex short pulse equation, Waves in Random and Complex Media, 32 (2022), 968-979.
  • [30] S. Malik, H. Almusawa, S. Kumar, A. M. Wazwaz, and M. S. Osman, A (2+ 1)-dimensional Kadomtsev–Petviashvili equation with competing dispersion effect: Painlev´e analysis, dynamical behavior and invariant solutions, Results in Physics, 23 (2021), 104043.
  • [31] R. C. Merton, Theory of rational option pricing, Bell J Econ Manage Sci 4, (1973), 141–183.
  • [32] R. Mia, M. M. Miah, and M. S. Osman, A new implementation of a novel analytical method for finding the analytical solutions of the (2+ 1)-dimensional KP-BBM equation, Heliyon, 9(5) (2023).
  • [33] J. Panos, L´evy Processes with Applications in Finance. LAP LAMBERT Academic Publishing, 2016.
  • [34] M. Raheel, K. K. Ali, A. Zafar, A. Bekir, O. A. Arqub, and M. Abukhaled, Exploring the Analytical Solutions to the Economical Model via Three Different Methods, Journal of Mathematics, (2023), 2023.
  • [35] R. U. Rahman, M. M. M. Qousini, A. Alshehri, S. M. Eldin, K. El-Rashidy, and M. S. Osman, Evaluation of the performance of fractional evolution equations based on fractional operators and sensitivity assessment, Results in Physics, (2023), 106537.
  • [36] H. Rezazadeh, K. K. Ali, S. Sahoo, J. Vahidi, and M. Inc, New optical soliton solutions to magneto-optic waveguides, Optical and Quantum Electronics,54(12) (2022), 801.
  • [37] S. Sahoo and S. S. Ray, Analysis of Lie symmetries with conservation laws for the (3+ 1) dimensional timefractional mKdV–ZK equation in ion-acoustic waves, Nonlinear Dynamics, 90 (2017), 1105-1113.
  • [38] S. Sahoo and S. S. Ray, Lie symmetries analysis and conservation laws for the fractional Calogero–Degasperis–Ibragimov–Shabat equation, International Journal of Geometric Methods in Modern Physics, 15(07) (2018), 1850110.
  • [39] S. Sahoo and S. S. Ray, The conservation laws with Lie symmetry analysis for time fractional integrable coupled KdV–mKdV system, International Journal of Non-linear Mechanics, 98 (2018), 114-121.
  • [40] S. San, A. R. Seadawy, and E. Yasar, Optical soliton solution analysis for the (2+ 1) dimensional KunduMukherjee-Naskar model with local fractional derivatives, Optical and Quantum Electronics, 54(7) (2022), 1-21.
  • [41] A. R. Seadawy and N. Cheemaa, Applications of extended modified auxiliary equation mapping method for highorder dispersive extended nonlinear Schro¨dinger equation in nonlinear optics, Modern Physics Letters B, 33(18) (2019), 1950203.
  • [42] A. R. Seadawy, M. Iqbal, and D. Lu, Applications of propagation of long-wave with dissipation and dispersion in nonlinear media via solitary wave solutions of generalized Kadomtsev–Petviashvili modified equal width dynamical equation, Computers Mathematics with Applications, 78(11) (2019), 3620-3632.
  • [43] I. Siddique, M. M. Jaradat, A. Zafar, K. B. Mehdi, and M. S. Osman, Exact traveling wave solutions for two prolific conformable M-Fractional differential equations via three diverse approaches, Results in Physics, 28 (2021), 104557.
  •  [44] J. V. Sousa and E. C. de Oliveira, A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties, Int. J. Anal. Appl., 16 (2018), 83–96.
  • [45] T. A. Sulaiman, G. Yel, and H. Bulut, M-fractional solitons and periodic wave solutions to the Hirota–Maccari system, Modern Physics Letters B, 33(05) (2019), 1950052.
  • [46] K. U. Tariq, H. Rezazadeh, M. Zubair, M.S. Osman, and Akinyemi,L. New Exact and Solitary Wave Solutions of Nonlinear Schamel–KdV Equation, International Journal of Applied and Computational Mathematics, 8(3) (2022), 114.
  • [47] S. Tarla, K. K. Ali, R. Yilmazer, and M. S. Osman, New optical solitons based on the perturbed Chen-Lee-Liu model through Jacobi elliptic function method, Optical and Quantum Electronics, 54(2) (2022), 1-12.
  • [48] A. Tripathy and S. Sahoo, New distinct optical dynamics of the beta-fractionally perturbed Chen–Lee–Liu model in fiber optics, Chaos, Solitons Fractals, 163 (2022), 112545.
  • [49] A. Tripathy, S. Sahoo, H. Rezazadeh, Z. P. Izgi, and M.S. Osman, Dynamics of damped and undamped wave natures in ferromagnetic materials, Optik, 281 (2023), 170817.
  • [50] J. Vanterler, D. A. C. Sousa, E. Capelas, and D. E. Oliveira, A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties, International Journal of Analysis and Applications, 16(1) (2018), 83-96.
  • [51] O. Vukovic, Interconnectedness of Schr¨odinger and Black-Scholes Equation, J. Appl. Math. Phys., 3(9) (2015), 1108–1113.
  • [52] Z. Yan, Vector financial rogue waves, Physics letters a, 375(48) (2011), 4274-4279.
  • [53] Y. Yue, L. He, and G. Liu, Modeling and application of a new nonlinear fractional financial model, Journal of Applied Mathematics, (2013), 2013.
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