In this paper‎, ‎a modern method is presented to solve a class of fractional optimal control problems (FOCPs) indirectly‎. ‎First‎, ‎the necessary optimality conditions for the FOCP are obtained in the form of two fractional differential equations (FDEs)‎. ‎Then‎, ‎the unknown functions are approximated by the hybrid functions‎, ‎including Bernoulli polynomials and Block-pulse functions based o...

We studied the kinetics of the use-dependent block of the Na+ current (INa) by disopyramide and lidocaine. INa was recorded from isolated guinea pig ventricular myocytes by using the whole-cell patch-clamp technique. The use-dependent block of INa by disopyramide with 20- and 200-msec depolarizing pulses developed in two exponential functions. The degree of the use-dependent block and the ampli...

The present work approaches the problem of achieving the approximate solution of the second order initial value problems (IVPs) via its conversion into a Volterra integral equation of the second kind (VIE2). Therefore, we initially solve the IVPs using Runge–Kutta of the forth–order method (RK), and then convert it into VIE2, and apply the εmodified block–pulse functions (εMBPFs) and their oper...

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...

Many different bases functions have been used to estimate the solution to differential equations, such as orthogonal bases [3, 4, 14, 15], wavelets [7–8] and hybrid [2, 13, 16–17]. The various systems of orthogonal functions may be classified into two categories. The first is piecewise continuous function (PCBF) to which the orthogonal systems of Walsh functions [5], Block-pulse functions [4, 1...

In this study, we present a direct method to solve nonlinear two-dimensional VolterraHammerestein integral equations in terms of twodimensional piecewise constant block-pulse functions (2D-PCBFs). Properties of these functions and operational matrix of integration together with the product operational matrix are presented and used to transform the integral equation to a matrix equation which co...