An analysis on the subject of “induced magnetic field effect on stagnation flow of a TiO2-Cu/water hybrid nanofluid over a stretching sheet” has been carried out in this paper. It should be noted that hybrid nanofluid consists of two or more types of nanoparticles along with a base fluid and it is used to increase the heat transfer. Furthermore, the non-linear differential equations modeling this issue are included in this article. In order to solve these equations numerically, Runge-Kutta Fehlberg method is used as a numerical method in this problem. The main objective of this paper is to investigate the effects of change in parameters of stretching ratio parameter (A∗), nanoparticles volumetric fractions (∅2), magnetic parameter (β) and reciprocal magnetic Prandtl number (λ) on the functions including velocity, induced magnetic field and temperature for both Cu-water nanofluid and TiO2-Cu/water hybrid nanofluid. Also Lorentz force which is derived from magnetic field is mentioned in this section. In addition, the impacts of (∅2), (β) and (λ) on the profiles of nanofluid and hybrid nanofluid temperature for three categories of nanoparticle shapes named brick, cylinders, and platelets are analyzed. At the end, the influences of (∅2), (β) and (λ) on skin friction coefficient (Cf) and Nusselt number (Nux) for Cu-water nanofluid and TiO2-Cu/water hybrid fluid for different nanoparticles shapes are discussed. In all of these studies it can be seen that applying platelets shaped nanoparticles is more effective. Display omitted •TiO2‐Cu/H2O hybrid nanofluid is incorporated.•Analysis of thermal conductivity of hybrid nanofluid is highlighted.•Different shape factors for nanoparticles are addressed.•Nonlinear differential equations are solved numerically.