This paper describes and compares application of wavelet basis and Block-Pulse functions (BPFs) for solving fractional integro-differential equation (FIDE) with a weakly singular kernel‎. ‎First‎, ‎a collocation method based on Haar wavelets (HW)‎, ‎Legendre wavelet (LW)‎, ‎Chebyshev wavelets (CHW)‎, ‎second kind Chebyshev wavelets (SKCHW)‎, ‎Cos and Sin wavelets (CASW) and BPFs are presented f...

We consider travelling periodic and quasi-periodic wave solutions of a set of coupled nonlinear Schrödinger equations. In fibre optics these equations can be used to model single mode fibers with strong birefingence and two-mode optical fibers. Recently these equations appear as model, which describe pulse-pulse interaction in wavelength-division-multiplexed channels of optical fiber transmissi...

The general properties of two-dimensional generalized Bessel functions are discussed. Various asymptotic approximations are derived and applied to analyze the basic structure of the two-dimensional Bessel functions as well as their nodal lines.

The four-dimensional Hodgkin–Huxley equations describe the propagation in space and time of the action potential v(z) along a neural axon with z = x+ ct and c being the pulse speed. The potential v(z), which is parameterized by the temperature, is driven by three gating functions, m(z), n(z) and h(z), each of which obeys formal first order kinetics with rate constants that are represented as no...

A new computational method based on Wilson wavelets is proposed for solving a class of nonlinear stochastic It^{o}-Volterra integral equations. To do this a new stochastic operational matrix of It^{o} integration for Wilson wavelets is obtained. Block pulse functions (BPFs) and collocation method are used to generate a process to forming this matrix. Using these basis functions and their operat...