In this paper, a three-stage fifth-order Runge-Kutta method for the integration of a special third-order ordinary differential equation (ODE) is constructed. The zero stability of the method is proven. The numerical study of a third-order ODE arising in thin film flow of viscous fluid in physics is discussed. The mathematical model of thin film flow has been solved using a new method and numerical comparisons are made when the same problem is reduced to a first-order system of equations which are solved using the existing Runge-Kutta methods. Numerical results have clearly shown the advantage and the efficiency of the new method.

An interesting quadratic fractional integral equation is investigated in this work via a generalized Mittag-Leffler (ML) function. The generalized ML–Hyers–Ulam stability is established in this investigation. We study both of the Hyers–Ulam stability (HUS) and ML–Hyers–Ulam–Rassias stability (ML-HURS) in detail for our proposed differential equation (DEq). Our proposed technique unifies various differential equations’ classes. Therefore, this technique can be further applied in future research works with applications to science and engineering.

The aim of the present study is to examine the convective heat transfer of nanofluid past a wedge subject to first-order chemical reaction, heat generation/absorption and suction effects. The influence of wedge angle parameter, thermophoresis, Dufour and Soret type diffusivity are included. The local similarity transformation is applied to convert the governing nonlinear partial differential equations into ordinary differential equations. Shooting method integrated with fourth-order Runge-Kutta method is used to solve the ordinary differential equations. The skin friction, heat and mass transfer rates as well as the effects of various parameters on velocity, temperature and solutal concentration profiles are analyzed. The results indicate that when the chemical reaction parameter increases, the heat transfer coefficient increases while the mass transfer coefficient decreases. The effect of chemical reaction parameter is very important in solutal concentration field compared to velocity and temperature profiles since it decreases the solutal concentration of the nanoparticle.

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