دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات45
تعداد شماره‌ها1,553
تعداد مقالات18,950
تعداد مشاهده مقاله63,789,709
تعداد دریافت فایل اصل مقاله23,335,827
Mehdi, Khush Bukht, Baloch, Sajawal Abbas, Siddique, Imran, Abduvalieva, Dilsora, Yaseen, Zaher, Ahmad, Hijaz. (1405). Modulation instability and solitary wave analysis of the Ivancevic option pricing model via Novel mathematical techniques. سامانه مدیریت نشریات علمی, 14(4), 1773-1798. doi: 10.22034/cmde.2025.67141.3185
Khush Bukht Mehdi; Sajawal Abbas Baloch; Imran Siddique; Dilsora Abduvalieva; Zaher M Yaseen; Hijaz Ahmad. "Modulation instability and solitary wave analysis of the Ivancevic option pricing model via Novel mathematical techniques". سامانه مدیریت نشریات علمی, 14, 4, 1405, 1773-1798. doi: 10.22034/cmde.2025.67141.3185
Mehdi, Khush Bukht, Baloch, Sajawal Abbas, Siddique, Imran, Abduvalieva, Dilsora, Yaseen, Zaher, Ahmad, Hijaz. (1405). 'Modulation instability and solitary wave analysis of the Ivancevic option pricing model via Novel mathematical techniques', سامانه مدیریت نشریات علمی, 14(4), pp. 1773-1798. doi: 10.22034/cmde.2025.67141.3185
Mehdi, Khush Bukht, Baloch, Sajawal Abbas, Siddique, Imran, Abduvalieva, Dilsora, Yaseen, Zaher, Ahmad, Hijaz. Modulation instability and solitary wave analysis of the Ivancevic option pricing model via Novel mathematical techniques. سامانه مدیریت نشریات علمی, 1405; 14(4): 1773-1798. doi: 10.22034/cmde.2025.67141.3185

Modulation instability and solitary wave analysis of the Ivancevic option pricing model via Novel mathematical techniques

Computational Methods for Differential Equations
مقاله 16، دوره 14، شماره 4، دی 2026، صفحه 1773-1798    اصل مقاله (10.99 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.67141.3185
نویسندگان
Khush Bukht Mehdi1؛ Sajawal Abbas Baloch2؛ Imran Siddique* 3؛ Dilsora Abduvalieva4؛ Zaher M Yaseen5؛ Hijaz Ahmad6
1Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan.
2Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan.
31. Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan. 2. Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan. 3. Mathematics in Applied Sciences and Engineering Research Group, Scientific Research Center, Al-Ayen University, Nasiriyah, 64001, Iraq.
4Department of Mathematics and Information Technologies, Tashkent State Pedagogical University, Bunyodkor avenue, 27, Tashkent, 100070, Uzbekistan.
5Civil and Environmental Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia.
61. Operational Research Center in Healthcare, Near East University, Nicosia/TRNC, 99138 Mersin 10, Turkey. 2. Department of Mathematics, College of Science, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, South Korea. 3. Engineered Biomaterials Research Center, Khazar University, Baku, Azerbaijan.
چکیده
In academia, financial engineering challenges are very important, and there is an ongoing demand for effective ways to examine and evaluate these models. The new extended direct algebraic approach and the new auxiliary equation method have been used in this study to investigate the analytical solutions of the economically significant model known as the Ivancevic option pricing model (IOPM) in the sense of a new definition of M-truncated derivative. Additionally, we will examine the equation’s modulation instability (MI) using linear stability approach that demonstrates the accuracy and stability of all combined solutions. The analytical method of this model is infrequently observed in the literature, despite the fact that numerous scholars have examined its applicability and feasibility. The regulated Brownian motion associated with a non-linear Schr¨odinger type equation is described by this model. Mathematical approaches are applied to generate the solution to understand the fluctuations in market prices for the proposed model. The reaction of system to pulse propagation is explained through the use of graphical representations in 2D, contour and 3D forms. Anticipating suitable parameter values that correspond with the observed data is made possible by these illustrations. The sensitivity analysis predicts the model’s dependence on the initial conditions. The findings of this study indicated that the suggested approaches preserved the physical characteristics present in realistic processes while providing a very dependable and adaptable substitute for problem-solving. Furthermore, we guarantee that all of the results demonstrate that these techniques are a useful mathematical tool for identifying precise solitary wave solutions to nonlinear models that are present in various scientific and technical domains.
کلیدواژه‌ها
Ivancevic option pricing model؛ M-truncated derivative؛ New extended direct algebraic method؛ New auxiliary equation method؛ Exact solutions؛ Modulation instability analysis
مراجع
  • [1] G. Adomian, On the modeling and analysis of a national economy, In Dynamic Modelling and Control of National Economies 1983 (pp. 189-196), (1984), Pergamon.
  • [2] K. K. Ahmed, N. M. Badra, H. M. Ahmed, and W. B. Rabie, Soliton solutions and other solutions for Kundu–Eckhaus equation with quintic nonlinearity and Raman effect using the improved modified extended tanh-function method, Mathematics, 10(22) (2022), 4203.
  • [3] A. Ali, J. Ahmad, and S. Javed, Exact soliton solutions and stability analysis to (3+ 1)-dimensional nonlinear Schrödinger model, Alexandria Engineering Journal, 76 (2023), 747-756.
  • [4] Y. F. Alharbi, M. A. Abdelrahman, M. A. Sohaly, and S. I. Ammar, Disturbance solutions for the long–short-wave interaction system using bi-random Riccati–Bernoulli sub-ODE method, J. Taibah Uni. Sci., 14(1) (2020), 500-506.
  • [5] K. K. Ali, S. B. G. Karakoc¸, and H. Rezazadeh, Optical soliton solutions of the fractional perturbed nonlinear Schrödinger equation, TWMS J. Appl. Engi. Math., 10(4) (2020), 930-939.
  • [6] F. Antonelli, Stability of backward stochastic differential equations, Stochas. Process. Appl., 62(1) (1996), 103-114.
  • [7] S. A. Baloch, M. Abbas, F. A. Abdullah, S. T. R. Rizvi, A. Althobaiti, and A. R. Seadawy, Multiple Soliton Solutions of Generalized Reaction Duffing Model Arising in Various Mechanical Systems, Inter. J. Theor. Phy., 63(9) (2024) 1-15.
  • [8] S. A. Baloch, M. Abbas, F. A. Abdullah, M. Elamin, and M. Elmahi, M-shaped rational, homoclinic breather, kink-cross rational, multi-wave and interactional soliton solutions to the fifth-order Sawada-Kotera equation, Partial Diff. Eqs. Appl. Math., 11 (2024), 100919.
  • [9] S. A. Baloch, M. Abbas, T. Nazir, and Y. S. Hamed, Lump, periodic, multi-waves and interaction solutions to non-linear Landau–Ginzburg–Higgs model, Optical and Quantum Electronics, 56(8) (2024), 1345.
  • [10] F. Black, and K. Scholes, The pricing of options and corporate liabilities, Journal of political economy, 81(3) (1973), 637-654.
  • [11] 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 (2021), 2539-2548.
  • [12] L. Cveticanin, Homotopy–perturbation method for pure nonlinear differential equation, Chaos, Solitons & Fractals, 30(5) (2006), 1221-1230.
  • [13] B. Decardi-Nelson, and J. Liu, Robust economic model predictive control with zone control, IFAC-PapersOnLine, 54(3) (2021), 237-242.
  • [14] S. O. Edeki, O. O. Ugbebor, and O. Gonzàlez-Gaxiola, Analytical solutions of the Ivancevic option pricing model with a nonzero adaptive market potential, Inter. J. Pure and Applied Math., 115(1) (2017), 187-198.
  • [15] E. Fan and J. Zhang, Applications of the Jacobi elliptic function method to special-type nonlinear equations, Physics Letters A, 305(6) (2002), 383-392.
  • [16] M. S. Ghayad, N. M. Badra, H. M. Ahmed, and W. B. Rabie, Derivation of optical solitons and other solutions for nonlinear Schrödinger equation using modified extended direct algebraic method, Alexandria Engin. J., 64 (2023), 801-811.
  • [17] A. K. Gupta and S. S. Ray, Comparison between homotopy perturbation method and optimal homotopy asymptotic method for the soliton solutions of Boussinesq–Burger equations,. Computers & Fluids, 103 (2014), 34-41.
  • [18] W. Hamali and A. A. Alghamdi, Exact solutions to the fractional nonlinear phenomena in fluid dynamics via the Riccati-Bernoulli sub-ODE method, AIMS Mathematics, 9(11) (2024), 31142-31162.
  • [19] H. H. Hussein, H. M. Ahmed, and W. Alexan, Analytical soliton solutions for cubic-quartic perturbations of the Lakshmanan-Porsezian-Daniel equation using the modified extended tanh function method, Ain Shams Engin. J., 15(3) (2024), 102513.
  • [20] S. Ibrahim, A. M. Ashir, Y. A. Sabawi, and D. Baleanu, Realization of optical solitons from nonlinear Schrödinger equation using modified Sardar sub-equation technique, Optical and Quantum Electronics, 55(7) (2023), 617.
  • [21] M. Inc, A. Yusuf, A. I. Aliyu, and D. Baleanu, Soliton solutions and stability analysis for some conformable nonlinear partial differential equations in mathematical physics, Optical and Quantum Electronics, 50 (2018), 1-14.
  • [22] A. Jhangeer, A. R. Ansari, M. Imran, M. B. Riaz, and A. M. Talafha, Application of propagating solitons to Ivancevic option pricing governing model and construction of first integral by Nucci’s direct reduction approach, Ain Shams Engi. J., 15(4) (2024), 102615.
  • [23] S. B. G. Karako¸c, L. Mei, and K. K. Ali, Two efficient methods for solving the generalized regularized long wave equation, Applicable Analysis, 101(13) (2022), 4721-4742.
  • [24] S. B. G. Karakoc and K. K. Ali, Theoretical and computational structures on solitary wave solutions of Benjamin Bona Mahony-Burgers equation, Tbilisi Mathematical Journal, 14(2) (2021), 33-50.
  • [25] S. B. G. Karakoc, K. K. Ali, and D. Y. Sucu, A new perspective for analytical and numerical soliton solutions of the Kaup–Kupershmidt and Ito equations, J. Compu. Appl. Math., 421 (2023), 114850.
  • [26] E. V. Krishnan, M. Al-Gabshi, Q. Zhou, K. R. Khan, M. F. Mahmood, Y. Xu, and M. Belic, Solitons in optical metamaterials by mapping method, J. Optoelectron. Adv. Mater., 17(3-4) (2015), 511-516.
  • [27] D. Kwon, The impacts of oil price shocks and United States economic uncertainty on global stock markets, Int. J. Finance & Economics, 27(2) (2022), 1595-1607.
  • [28] J. Luo, C. Zhao, Q. Chen, and G. Li, Using deep belief network to construct the agricultural information system based on Internet of Things, The Journal of Supercomputing, 78(1) (2022), 379-405.
  • [29] A. Mahmood, H. M. Srivastava, M. Abbas, F. A. Abdullah, P. O. Mohammed, D. Baleanu, and N. Chorfi, Optical soliton solutions of the coupled Radhakrishnan-Kundu-Lakshmanan equation by using the extended direct algebraic approach, Heliyon, 9(10) (2023).
  • [30] J. Manafian and N. Allahverdiyeva, An analytical analysis to solve the fractional differential equations, Advanced Mathematical Models & Application, 6(2) (2021), 128-161.
  • [31] K. S. Miller and B. Ross, An introduction to the fractional calculus and fractional differential equations, (1993).
  • [32] M. Mirzazadeh, Modified simple equation method and its applications to nonlinear partial differential equations, Infor. Sci. Lett., 3(1) (2014), 1.
  • [33] M. A. S. Murad, H. F. Ismael, F. K. Hamasalh, N. A. Shah, and S. M. Eldin, Optical soliton solutions for time-fractional Ginzburg–Landau equation by a modified sub-equation method, Results in Physics, 53, (2023), 106950.
  • [34] K. Oldham and J. Spanier, The fractional calculus theory and applications of differentiation and integration to arbitrary order (1974), Elsevier.
  • [35] I. Podlubny, Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Elsevier, (1998).
  • [36] W. B. Rabie and H. M. Ahmed, Dynamical solitons and other solutions for nonlinear Biswas–Milovic equation with Kudryashov’s law by improved modified extended tanh-function method, Optik, 245 (2021), 167665.
  • [37] 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(1) (2023), 1416097.
  • [38] H. U. Rehman, M. S. Saleem, M. Zubair, S. Jafar, and I. Latif, Optical solitons with Biswas–Arshed model using mapping method, Optik, 194 (2019), 163091.
  • [39] R. J. Rendleman, Two-state option pricing. The Journal of Finance, Journal of Finance, 34(5) (1979), 1093-1110.
  • [40] Y. Saglam Ozkan and E. Yasar, Prolific new M-fractional soliton behaviors to the Schrödinger type Ivancevic option pricing model by two efficient techniques, Comput. Meth. Diff. Equa., 12(2) (2024), 207-225.
  • [41] S. Saifullah, S. Ahmad, M. A. Alyami, and M. Inc, Analysis of interaction of lump solutions with kink-soliton solutions of the generalized perturbed KdV equation using Hirota-bilinear approach, Physics Letters A, 454 (2022), 128503.
  • [42] N. Shahid, M. Z. Baber, T. S. Shaikh, G. Iqbal, N. Ahmed, A. Akgül, and M. De la Sen, Dynamical study of groundwater systems using the new auxiliary equation method, Results in Physics, 58 (2024), 107444.
  • [43] K. P. Sharp, Stochastic differential equations in finance, Appl. Math. Compu., 37(2) (1990), 131-148.
  • [44] I. Siddique, K. B. Mehdi, F. Jarad, M. E. Elbrolosy, and A. A. Elmandouh, Novel precise solutions and bifurcation of traveling wave solutions for the nonlinear fractional (3+ 1)-dimensional WBBM equation. Inter. J. Modern Phys. B, 37(02) (2023), 2350011.
  • [45] F. Tasnim, M. A. Akbar, and M. S. Osman, The extended direct algebraic method for extracting analytical solitons solutions to the cubic nonlinear Schrödinger equation involving beta derivatives in space and time, Fractal and Fractional, 7(6) (2023), 426.
  • [46] N. K. Vitanov, Simple Equations Method (SEsM): An effective algorithm for obtaining exact solutions of nonlinear differential equations, Entropy, 24(11) (2022), 1653.
  • [47] M. Vivas-Cortez, S. A. Baloch, M. Abbas, M. Alosaimi, and G. Wei, Lump, Breather, Ma-Breather, Kuznetsov–Ma-Breather, Periodic Cross-Kink and Multi-Waves Soliton Solutions for Benney–Luke Equation, Symmetry, 16(6) (2024), 747.
  • [48] S. Wang, Novel soliton solutions of CNLSEs with Hirota bilinear method. Journal of Optics, 52(3) (2023), 1602-1607.
  • [49] E. M. Zayed and M. E. Elshater, Jacobi elliptic solutions, soliton solutions and other solutions to four higher-order nonlinear Schrödinger equations using two mathematical methods, Optik, 131 (2017), 1044-1062.
  • [50] X. Z. Zhang, I. Siddique, K. B. Mehdi, A. A. Elmandouh, and M. Inc, Novel exact solutions, bifurcation of nonlinear and supernonlinear traveling waves for M-fractional generalized reaction Duffing model and the density dependent M-fractional diffusion reaction equation, Results in Physics, 37 (2022), 105485.
  • [51] X. Zhang, X. Yang, and Q. He, Multi-scale systemic risk and spillover networks of commodity markets in the bullish and bearish regimes, The North American J. Econo. Finance, 62 (2022), 101766.
  • [52] C. Zhu, M. Al-Dossari, S. Rezapour, S. A. M. Alsallami, and B. Gunay, Bifurcations, chaotic behavior, and optical solutions for the complex Ginzburg–Landau equation, Results in Physics, 59 (2024), 107601.
آمار
تعداد مشاهده مقاله: 342
تعداد دریافت فایل اصل مقاله: 493


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب