In this paper, an effective technique is proposed to determine thenumerical solution of nonlinear Volterra-Fredholm integralequations (VFIEs) which is based on interpolation by the hybrid ofradial basis functions (RBFs) including both inverse multiquadrics(IMQs), hyperbolic secant (Sechs) and strictly positive definitefunctions. Zeros of the shifted Legendre polynomial are used asthe collocatio...

The recursive formulas of modified Bessel functions give the relativistic expressions for energy and momentum. Modified Bessel functions are solutions to a continuous time, one-dimensional discrete jump process. The jump process is analyzed from two inertial frames with a relative constant velocity; the average distance of a particle along the chain corresponds to the distance between two obser...

A new Perceptron training algorithm is presented, which employs the piecewise linear activation function and the sum of squared differences error function over the entire training set. The most commonly used activation functions are continuously differentiable such as the logistic sigmoid function, the hyperbolic-tangent and the arctangent. The differentiable activation functions allow gradient...

The attitude coordination control problem for formation flying spacecraft associated with time-varying reference attitude tracking subject to control input saturation is investigated in this paper. According to different cases, three kinds of continuous and bounded coordination controllers are proposed. With the use of hyperbolic tangent functions, a fundamental controller is presented for an i...

In this paper, the hyperbolic tangent function method is applied for constructing exact solutions space-time conformal fractional Burgers’ equation. Furthermore, equation tested Painlevé property, and consequently, new numerous are generated via Bäcklund transform.