Existence of Solutions to a System of Fractional Differential Equations With Applications to Beam Deflections (European Journal of Pure and Applied Mathematics, 2025)
In this manuscript, we introduce a novel system of fractional differential equations incorporating both Caputo and conformable derivatives. We delve into the existence and uniqueness of solutions for this system, employing fixed-point techniques under appropriate conditions. To illustrate the practical applications of our theoretical findings, we investigate the traveling wave solutions of a tripled system of conformable fractional differential equations. Our analysis provides valuable insights into the dynamics and behavior of complex systems modeled by fractional differential equations.
Keywords: Nonlinear system, fractional derivative, Tanh’s method, traveling wave solution, evaluation metrics.