Optimal systems, series solutions and conservation laws for a time fractional cancer tumor model

Authors: Simon, S. G., Bira, B., & Zeidan, D.

Journal: Chaos, Solitons & Fractals, 169, 113311 (2023)

Impact Factor: 5.3 (Q1; SCIE)

DOI: https://doi.org/10.1016/j.chaos.2023.113311

Abstract: In this paper, we investigate a time-fractional cancer tumor model using Lie symmetry analysis. We derive the optimal systems of one-dimensional subalgebras and use them to obtain invariant solutions. We also develop series solutions for the model and analyze conservation laws to understand the physical properties of the system.

Classical and non-classical symmetries of time-fractional Navier–Stokes equation

Authors: Simon, S. G., & Bira, B.

Journal: Indian Journal of Physics, 98(7), 2475-2483 (2024)

Impact Factor: 1.6 (Q3; SCIE)

DOI: https://doi.org/10.1007/s12648-023-03010-5

Abstract: This paper presents a comprehensive analysis of both classical and non-classical symmetries for the time-fractional Navier-Stokes equation. We derive the determining equations and solve them to obtain the symmetry generators. The symmetry reductions lead to solutions that provide insights into the behavior of fractional fluid dynamics.

Lie Symmetries With Exact Solution for Time‐Fractional Foam Drainage Equation

Authors: Simon, S. G., & Bira, B.

Journal: Mathematical Methods in the Applied Sciences, 48(5), 5474-5482 (2025)

Impact Factor: 2.1 (Q1; SCIE)

DOI: https://doi.org/10.1002/mma.10612

Abstract: We apply Lie symmetry methods to analyze the time-fractional foam drainage equation. The symmetry generators are determined and used to reduce the equation to ordinary differential equations. Exact solutions are derived and their physical significance in foam dynamics is discussed.

Optimal algebras and novel solutions of time-fractional (2+1 – D) European call option model

Authors: Simon, S. G., Bira, B., & Thambiayya, S.

Journal: Discrete Dynamics in Nature and Society, 2025 (1), 5568285 (2025)

Impact Factor: 1.2 (Q3; SCIE)

DOI: https://doi.org/10.1155/ddns/5568285

Abstract: This paper investigates the time-fractional (2+1-dimensional) European call option model using optimal algebra techniques. We derive novel analytical solutions and examine their financial implications for option pricing in fractional market models.

Symmetry analysis, exact solutions and conservation laws of time fractional reaction-diffusion system occurring in diffusive flows

Authors: Simon, S. G., Bira, B., & Shagolshem, S.

Journal: Physics of Fluids, 2025 (Accepted for publication)

Impact Factor: 4.3 (Q1; SCIE)

Abstract: We present a comprehensive symmetry analysis of a time-fractional reaction-diffusion system that models diffusive flows. The study includes derivation of exact solutions and conservation laws, providing insights into the physical behavior of fractional diffusion processes.