Gimnitz Simon's
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Last updated: July 2, 2025
Send e-mail: gimnitz@gmail.com
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Gimnitz Simon'sPageWelcome!Last updated: July 2, 2025 Send e-mail: gimnitz@gmail.com |
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RESEARCH OVERVIEWMy research is focused on the application of Lie symmetry methods to fractional differential equations. I am particularly interested in developing analytical and numerical techniques for solving complex nonlinear fractional differential equations that arise in various fields of science and engineering. RESEARCH TITLELie group analysis to some fractional differential equations RESEARCH DESCRIPTIONMy research explores nonlinear differential equations with fractional order. Lie symmetry is used to reduce complicated partial differential equations into simpler solvable ordinary differential equations under invariance. Further, we analyse our reduced model under various methods to obtain solutions. Furthermore, we derive conserved vectors using symmetries. RESEARCH INTERESTS
CURRENT RESEARCH PROJECTSLie Symmetry Analysis of Fractional Cancer Tumor ModelsThis project involves the application of Lie symmetry methods to analyze and solve fractional-order differential equations that model cancer tumor growth. We derive optimal systems, series solutions, and conservation laws for these models. Related Publication: Simon, S. G., Bira, B., & Zeidan, D. (2023). Optimal systems, series solutions and conservation laws for a time fractional cancer tumor model. Chaos, Solitons & Fractals, 169, 113311. Symmetry Analysis of Fractional Navier-Stokes EquationsThis research focuses on applying both classical and non-classical symmetry methods to time-fractional Navier-Stokes equations. We investigate the invariance properties and derive solutions using symmetry reduction techniques. Related Publication: Simon, S. G., & Bira, B. (2024). Classical and non-classical symmetries of time-fractional Navier–Stokes equation. Indian Journal of Physics, 98(7), 2475-2483. Lie Symmetries for Fractional Foam Drainage EquationsThis project investigates the application of Lie symmetry methods to time-fractional foam drainage equations. We derive exact solutions and analyze the physical implications of these solutions. Related Publication: Simon, S. G., & Bira, B. (2024). Lie Symmetries With Exact Solution for Time‐Fractional Foam Drainage Equation. Mathematical Methods in the Applied Sciences. Optimal Algebras for Fractional European Call Option ModelsThis research focuses on deriving optimal algebras and novel solutions for time-fractional (2+1 – D) European call option models. We apply Lie symmetry methods to analyze these financial models. Related Publication: Simon, S. G., Bira, B., & Thambiayya, S. (2025). Optimal algebras and novel solutions of time-fractional (2+1 – D) European call option model. Discrete Dynamics in Nature and Society, 2025 (1), 5568285. Symmetry Analysis of Time-Fractional Reaction-Diffusion SystemsThis research investigates the symmetry analysis, exact solutions, and conservation laws of time-fractional reaction-diffusion systems that occur in diffusive flows. We apply advanced mathematical techniques to understand the behavior of these complex systems. Related Publication: Simon, S. G., Bira, B., & Shagolshem, S. (2025). Symmetry analysis, exact solutions and conservation laws of time fractional reaction-diffusion system occurring in diffusive flows. Physics of Fluids, 2025 (Accepted for publication). REVIEWING SERVICESI serve as a reviewer for the following journals:
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Mr. Gimnitz Simon S. Disclaimer: The views and opinions expressed in this website are strictly those of the author. The contents have not been reviewed or approved by SRM Institute of Science and Technology. |