In this paper, firstly, in $E_1^3$, we defined normal Fermi-Walker derivative and applied for the adapted frame. Normal Fermi-Walker parallelism, normal non-rotating frame, and Darboux vector expressions of normal Fermi-Walker derivative by normal Fermi-Walker derivative are given for adapted frame. Being conditions of normal Fermi-Walker derivative and normal non-rotating frame are examined fo...

The solution y(x) of an IVP for a linear ODE with analytic coefficient functions is represented as a power series. A high–order Taylor polynomial is used for an approximate numerical solution. The Taylor remainder series is rigorously estimated by some geometric series. The method has been implemented and tested on a computer. Guaranteed enclosures are achieved by taking into account all roundo...

Sufficient conditions are given for the existence of oscillatory proper solutions of a differential equation with quasiderivatives Lny = f(t, L0y, . . . , Ln−1y) under the validity of the sign condition f(t, x1, . . . , xn)x1 ≤ 0, f(t, 0, x2, . . . , xn) = 0 on R+ × Rn.

In this paper, we consider the oscillation criteria for even order nonlinear neutral differential equations of the form

The solution of differential equations is an important problem that arises in a host of areas. Many differential equations are too difficult to solve in closed form. Instead, it becomes necessary to employ numerical techniques. Differential equations have a major application in understanding physical systems that involve aerodynamics, fluid dynamics, thermodynamics, heat diffusion, mechanical o...

In this work an existence theorem for nth-order ordinary differential inclusions is proved without the continuity of multi-valued functions. Our results are an improvement upon the existence results of Dhage et al. [B.C. Dhage, T.L. Holambe, S.K. Ntouyas, Upper and lower solutions for second order discontinuous differential inclusions, Math. Sci. Res. J. 7 (5) (2003) 206–212] and Agarwal et al....

In the present article, we implement the new iterative method with a reliable algorithm to solve the nth-order linear/ nonlinear integro-differential equations. The obtained results confirm the power of the method in reducing the size of calculations compared with the other methods.