Eidinejad, ZahraSaadati, RezaVahidi, JavadLi, ChenkuanAllahviranloo, Tofigh2025-04-162025-04-162024Eidinejad, Z., Saadati, R., Vahidi, J., Li, C., & Allahviranloo, T. (2024). The existence of a unique solution and stability results with numerical solutions for the fractional hybrid integro-differential equations with Dirichlet boundary conditions. Boundary Value Problems, 2024(1), 120.16872762http://dx.doi.org/10.1186/s13661-024-01928-1https://hdl.handle.net/20.500.12713/6064In this paper, we investigate the fractional hybrid integro-differential equations with Dirichlet boundary conditions. We first prove the existence of a unique solution for the equation using a fixed point technique. Our main goal is to obtain the best approximation using optimal controllers. After studying the stability, we present the reproducing kernel Hilbert space numerical method to obtain approximate solutions to the equation. We finally conclude with numerical results. © The Author(s) 2024.eninfo:eu-repo/semantics/openAccess34A0835Q9235R1146E2292C32Existence of a unique solutionFractional hybrid integro-differential equationsOptimal control functionReproducing kernel Hilbert space methodStabilityArticle2024110.1186/s13661-024-01928-1Q1