(untitled) (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.