A new mixed fractional derivative is introduced, combining singular and non-singular kernels. This derivative generalizes several existing fractional derivatives, including Riemann–Liouville, Caputo, Caputo–Fabrizio, Atangana–Baleanu, and generalized Hattaf derivatives. The associated fractional integral is rigorously defined, and a novel numerical scheme is developed to approximate solutions of fractional differential equations (FDEs) involving this derivative. The study also presents an application in computational biology. The new mixed fractional derivative is defined in both Caputo and Riemann–Liouville senses. In the Caputo sense, it is expressed as an integral involving the Wiman function (Mittag–Leffler function) and a weight function. In the Riemann–Liouville sense, it involves differentiation of an integral with the same function. The derivative encompasses various existing fractional derivatives by adjusting parameters such as the kernel type, weight function, and order of differentiation. The Laplace transform of the new mixed fractional derivative is derived, which is essential for solving FDEs analytically. The study also provides properties and formulas for the new differential and integral operators. A numerical method based on Lagrange polynomial interpolation is developed to approximate solutions of FDEs with the new mixed fractional derivative. An application in computational biology is presented, demonstrating the utility of the new derivative in modeling complex biological systems. The study concludes that the new mixed fractional derivative offers a flexible and powerful tool for modeling systems with memory effects and hereditary characteristics, with potential applications in various scientific and engineering fields.A new mixed fractional derivative is introduced, combining singular and non-singular kernels. This derivative generalizes several existing fractional derivatives, including Riemann–Liouville, Caputo, Caputo–Fabrizio, Atangana–Baleanu, and generalized Hattaf derivatives. The associated fractional integral is rigorously defined, and a novel numerical scheme is developed to approximate solutions of fractional differential equations (FDEs) involving this derivative. The study also presents an application in computational biology. The new mixed fractional derivative is defined in both Caputo and Riemann–Liouville senses. In the Caputo sense, it is expressed as an integral involving the Wiman function (Mittag–Leffler function) and a weight function. In the Riemann–Liouville sense, it involves differentiation of an integral with the same function. The derivative encompasses various existing fractional derivatives by adjusting parameters such as the kernel type, weight function, and order of differentiation. The Laplace transform of the new mixed fractional derivative is derived, which is essential for solving FDEs analytically. The study also provides properties and formulas for the new differential and integral operators. A numerical method based on Lagrange polynomial interpolation is developed to approximate solutions of FDEs with the new mixed fractional derivative. An application in computational biology is presented, demonstrating the utility of the new derivative in modeling complex biological systems. The study concludes that the new mixed fractional derivative offers a flexible and powerful tool for modeling systems with memory effects and hereditary characteristics, with potential applications in various scientific and engineering fields.