Abbas F, Raza A, Zaman F, Baloch SA (2026) Biological Solitons in Biomembranes: Analytical Solutions of a Boussinesq-Type Equation with Amplitude-Dependent Nonlinearity. REVISTA INTERNACIONAL DE METODOS NUMERICOS PARA CALCULO Y DISENO EN INGENIERIA, 42(1)

AbdelSalam HM (2025) Geometric Analysis and Enhanced Approach for Addressing the Generalized M-Truncated Space-Time Fractional Burgers Model. Appl Math 19(3):531–540

Google Scholar 

Ahmad J, Hameed M, Mustafa Z, Rehman SU (2025) Soliton patterns in the truncated M-fractional resonant nonlinear Schrödinger equation via modified Sardar sub-equation method. J Opt 54(3):1118–1139

Article  Google Scholar 

Ahmad J, Hameed M, Mustafa Z, Ali A (2024) Symbolic computation and physical validation of optical solitons in nonlinear models. Opt Quant Electron 56(6):1026

Article  Google Scholar 

Ahmad J, Mustafa Z, Hameed M, Alkarni S, Shah NA (2024) Dynamics characteristics of soliton structures of the new (3+ 1) dimensional integrable wave equations with stability analysis. Results Phys 57:107434

Article  Google Scholar 

Al-Ghafri KS, Krishnan EV, Biswas A (2022) Cubic-quartic optical soliton perturbation and modulation instability analysis in polarization-controlled fibers for Fokas-Lenells equation. J Eur Opt Soc-Rapid Publ 18(2):9

Article  Google Scholar 

Alam MN, Akash HS, Saha U, Hasan MS, Parvin MW, Tunç C (2023) Bifurcation analysis and solitary wave analysis of the nonlinear fractional soliton neuron model. Iranian J Sci 47(5):1797–1808

Article  Google Scholar 

Ali A, Ahmad J, Javed S (2024) Dynamic investigation to the generalized Yu-Toda-Sasa-Fukuyama equation using Darboux transformation. Opt Quant Electron 56(2):166

Article  Google Scholar 

Ali KK, Maneea M (2023) New approximation solution for time-fractional Kudryashov-Sinelshchikov equation using novel technique. Alex Eng J 72:559–572

Article  Google Scholar 

Ali A, Ahmad J, Javed S (2023) Analysis of chaotic structures, bifurcation and soliton solutions to fractional Boussinesq model. Phys Scr 98(7):075217

Article  CAS  Google Scholar 

Amin MR, Hakim MA, Ullah MS (2025) Analysis of soliton behavior and overlap phenomena in the integrable beta-fractional Akbota equation with stability evaluation of equilibrium points. AIP Advances, 15(12)

Arora G, Pant R, Emadifar H, Khademi M (2023) Numerical solution of fractional relaxation-oscillation equation by using residual power series method. Alex Eng J 73:249–257

Article  Google Scholar 

Arshed S, Akram G, Sadaf M, Nabi AU, Alzaidi AS (2024) Optical soliton solutions of perturbed nonlinear Schrödinger equation with parabolic law nonlinearity. Opt Quant Electron 56(1):50

Article  Google Scholar 

Baloch SA, Mehdi KB, Ali R, Siddique I, Abduvalieva D (2025) Exploring solitary wave solutions in the Ivancevic option pricing model using a \(\phi ^6\)-model fractional derivative technique. J Nonlinear Complex Data Sci 26(5):265–287

Article  Google Scholar 

Batool F, Suleman MS, Demirbilek U, Rezazadeh H, Khedher KM, Alsulamy S, Ahmad H (2024) Studying the impacts of M-fractional and beta derivatives on the nonlinear fractional model. Opt Quant Electron 56(2):164

Article  Google Scholar 

Chahlaoui Y, Ali A, Javed S (2024) Study the behavior of soliton solution, modulation instability and sensitive analysis to fractional nonlinear Schrödinger model with Kerr Law nonlinearity. Ain Shams Engineering Journal 15(3):102567

Article  Google Scholar 

Chakrabarty AK, Roshid MM, Rahaman MM, Abdeljawad T, Osman MS (2024) Dynamical analysis of optical soliton solutions for CGL equation with Kerr law nonlinearity in classical, truncated M-fractional derivative, beta fractional derivative, and conformable fractional derivative types. Results Phys 60(107636):10–1016

Google Scholar 

Cheng F, Li J, Yu Q (2023) The existence of solitary wave solutions for the neuron model with conductance-resistance symmetry. AIMS Math 8(2):3322–3337

Article  Google Scholar 

Djennadi S, Shawagfeh N, Osman MS, Gómez-Aguilar JF, Arqub OA (2021) The Tikhonov regularization method for the inverse source problem of time fractional heat equation in the view of ABC-fractional technique. Phys Scr 96(9):094006

Article  CAS  Google Scholar 

Elmandouh A (2025a) Dynamical Analysis of a Soliton Neuron Model: Bifurcations, Quasi-Periodic Behaviour, Chaotic Patterns, and Wave Solutions. Mathematics 13(12):1912

Article  Google Scholar 

Elmandouh A (2025b) Dynamical Analysis of a Soliton Neuron Model: Bifurcations, Quasi-Periodic Behaviour, Chaotic Patterns, and Wave Solutions. Mathematics 13(12):1912

Article  Google Scholar 

Fan E, Zhang H (1998) A note on the homogeneous balance method. Phys Lett A 246(5):403–406

Article  CAS  Google Scholar 

Faridi WA, Tipu GH, Myrzakulova Z, Myrzakulov R, Akinyemi L (2024) Formation of optical soliton wave profiles of Shynaray-IIA equation via two improved techniques: a comparative study. Opt Quant Electron 56(1):132

Article  Google Scholar 

Heimburg T, Jackson AD (2005) On soliton propagation in biomembranes and nerves. Proc Natl Acad Sci 102(28):9790–9795

Article  CAS  PubMed  PubMed Central  Google Scholar 

Hosseini K, Hincal E, Salahshour S, Mirzazadeh M, Dehingia K, Nath BJ (2023) On the dynamics of soliton waves in a generalized nonlinear Schrödinger equation. Optik 272:170215

Article  CAS  Google Scholar 

Iqbal MA, Wang Y, Miah MM, Osman MS (2021) Study on date-Jimbo-Kashiwara-Miwa equation with conformable derivative dependent on time parameter to find the exact dynamic wave solutions. Fractal and Fractional 6(1):4

Article  Google Scholar 

Jawad AJM, Abu-AlShaeer MJ (2023) Highly dispersive optical solitons with cubic law and cubic-quintic-septic law nonlinearities by two methods. Al-Rafidain J Eng Sci 1(1):1–8

Google Scholar 

Johnson AS, Winlow W (2018) The soliton and the action potential-primary elements underlying sentience. Front Physiol 9:779

Article  PubMed  PubMed Central  Google Scholar 

Khater MM (2023a) RETRACTED: Soliton propagation under diffusive and nonlinear effects in physical systems;(1+ 1)-dimensional MNW integrable equation

Khater MM (2023b) Characterizing shallow water waves in channels with variable width and depth; computational and numerical simulations. Chaos Solitons Fractals 173:113652

Article  Google Scholar 

Khater MM (2023c) Novel computational simulation of the propagation of pulses in optical fibers regarding the dispersion effect. Int J Mod Phys B 37(09):2350083

Article  Google Scholar 

Khater MM (2023d) A hybrid analytical and numerical analysis of ultra-short pulse phase shifts. Chaos Solitons Fractals 169:113232

Article  Google Scholar 

Khater MM (2023e) Prorogation of waves in shallow water through unidirectional Dullin-Gottwald-Holm model; computational simulations. Int J Mod Phys B 37(08):2350071

Article  Google Scholar 

Lu X, Zhou Y, He D, Zheng F, Tang K, Tang J (2022) A novel two-variable optimization algorithm of TCA for the design of face gear drives. Mech Mach Theory 175:104960

Article  Google Scholar 

Majid SZ, Sağlam FNK, Ullah MS (2026) Comparison of neural and traditional techniques for soliton structures and dynamical behavior in a double-chain DNA model. Sci Rep

Mamunur Roshid M, Rahman M, Uddin M, Or Roshid H (2024) Modulation instability, analytical, and numerical studies for integrable time fractional nonlinear model through two explicit methods. Adv Math Phys 2024(1):6420467

Article  Google Scholar 

Mohyud-Din ST, Noor MA, Noor KI (2009) Modified variational iteration method for solving Sine Gordon equations. World Appl Sci J 6(7):999–1004

Google Scholar 

Mubaraki AM, Nuruddeen RI, Ali KK, Gómez-Aguilar JF (2024) Additional solitonic and other analytical solutions for the higher-order Boussinesq-Burgers equation. Opt Quant Electron 56(2):165

Article  Google Scholar 

Murad MAS, Ismael HF, Hamasalh FK, Shah NA, Eldin SM (2023) Optical soliton solutions for time-fractional Ginzburg-Landau equation by a modified sub-equation method. Results Phys 53:106950

Article  Google Scholar 

Osman MS (2019) New analytical study of water waves described by coupled fractional variant Boussinesq equation in fluid dynamics. Pramana 93(2):26

Article  Google Scholar 

Qayyum M, Ahmad E, Ali MR (2024) New solutions of time-fractional cancer tumor models using modified he-laplace algorithm. Heliyon, 10(14)

Qiu S, Shi M, Yousof H, Soon W, Jia M, Xue X, Dou X (2023) Solitary wave characteristics on the fine structure of the mesospheric sporadic sodium layer. Front Astronomy Space Sci 10:1241663

Article  Google Scholar 

Rahaman MS, Ullah MS, Islam MN (2025) Novel dynamics of the nonlinear fractional soliton neuron model with sensitivity analysis. AIP Adv, 15(8)

Rehman SU, Ahmad J (2023) Diverse optical solitons to nonlinear perturbed Schrödinger equation with quadratic-cubic nonlinearity via two efficient approaches. Phys Scr 98(3):035216

Article  Google Scholar 

Roshid MM, Rahman MM, Roshid HO, Bashar MH (2024) A variety of soliton solutions of time M-fractional: Non-linear models via a unified technique. PLoS ONE 19(4):e0300321

Article  CAS  PubMed  PubMed Central  Google Scholar 

Seadawy AR, Ali A, Bekir A (2025) Solitary wave solutions of the nonlinear fractional soliton neuron model via application of five mathematical methods. Mod Phys Lett B 39(23):2550098

Article  CAS  Google Scholar 

Sousa JVDC, de Oliveira EC (2017) A new truncated \(M\)-fractional derivative type unifying some fractional derivative types with classical properties. arXiv preprint arXiv:1704.08187

Stefani S, Piccioni G, Poulet F, Filacchione G, Vincendon M, Barbis A, Lecomte B (2025) Calibration of MAJIS (Moons and Jupiter Imaging Spectrometer): VI. The inflight calibration unit (ICU). Review of Scientific Instruments, 96(1)

Tariq MM, Riaz MB, Aziz-ur-Rehman M (2024) Investigation of space-time dynamics of Akbota equation using Sardar sub-equation and Khater methods: unveiling bifurcation and chaotic structure. Int J Theor Phys 63(8):210

Article  Google Scholar