Wavelets and radial basis functions (RBFs) lead to two distinct ways of representing signals in terms of shifted basis functions. RBFs, unlike wavelets, are nonlocal and do not involve any scaling, which makes them applicable to nonuniform grids. Despite these fundamental differences, we show that the two types of representation are closely linked together . . . through fractals. First, we iden...

approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. in this paper with central difference approximation and newton cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. three...

In this paper, we investigate the numerical study of nonlinear Fredholm integro-differential equation with fractional Caputo-Fabrizio derivative. We use Hermite wavelets and collocation technique to approximate exact solution by reducing a algebraic system. Furthermore, apply method on certain examples check its accuracy validity.

A finite difference/Galerkin spectral discretization for the temporal and spatial fractional coupled Ginzburg–Landau system is proposed analyzed. The Alikhanov L2-1? difference formula utilized to discretize time Caputo derivative, while Legendre-Galerkin approximation used approximate Riesz operator. scheme shown efficiently applicable with accuracy in space second-order time. discrete form of...

Abstract We describe an expansion of Legendre polynomials, analogous to the Taylor expansion, to approximate arbitrary functions. We show that the polynomial coefficients in Legendre expansion, thus, the whole series, converge to zero much more rapidly compared to the Taylor expansion of the same order. Furthermore, using numerical analysis with sixth-order polynomial expansion, we demonstrate ...

In a recent paper, Cohl and Costas-Santos derived number of interesting multi-derivative multi-integral relations for the associated Legendre Ferrers functions in which orders those are changed integral steps. These potential use physical problems. We show here how their results can be simply from more general involving non-integer changes order obtained using fractional group operator methods ...

In this paper, a numerical approach for solving systems of nonlinear fractional differential equations (FDEs) is presented Using the Euler wavelets technique and associated operational matrices integration, we try to solve those FDEs. The method’s major objective transform FDE into system algebraic that straightforward with matrix techniques. are constructed using polynomials, which have fewer ...

In this paper, we consider the Legendre spectral Galerkin and Legendre spectral collocation methods to approximate the solution of Urysohn integral equation. We prove that the approximated solutions of the Legendre Galerkin and Legendre collocation methods converge to the exact solution with the same orders, O(n−r) in L2-norm and O(n 1 2 −r) in infinity norm, and the iterated Legendre Galerkin ...

this paper concerns the problem of robust stabilization of uncertain fractional-order non-autonomous systems. in this regard, a single input active control approach is proposed for control and stabilization of three-dimensional uncertain fractional-order systems. the robust controller is designed on the basis of fractional lyapunov stability theory. furthermore, the effects of model uncertainti...