The solution of a partial differential equation can be obtained by computing the inverse
operator map between the input and the solution space. Towards this end, we introduce a …

In this note, we review some important results on wavelets, together with their main
applications. Similarly, we present the main results on fractional calculus and their current …

This paper deals with Chebyshev wavelets. We analyze their properties computing their
Fourier transform. Moreover, we discuss the differential properties of Chebyshev wavelets …

According to the various and extensive applications of fractional calculus in a range of fields,
such as engineering, biology, image processing, material science and economics …

In the current study, new functions called generalized fractional-order Bernoulli wavelet
functions (GFBWFs) based on the Bernoulli wavelets are defined to obtain the numerical …

Fractional differential equations are solved using the Legendre wavelets. An operational
matrix of fractional order integration is derived and is utilized to reduce the fractional …

In this paper, we first construct the second kind Chebyshev wavelet. Then we present a
computational method based on the second kind Chebyshev wavelet for solving a class of …

In this paper, a new numerical method for solving fractional differential equations is
presented. The fractional derivative is described in the Caputo sense. The method is based …

In this paper, the second kind Chebyshev wavelet method is presented for solving linear and
nonlinear fractional differential equations. We first construct the second kind Chebyshev …

In this paper, an efficient and accurate computational method based on the Legendre
wavelets (LWs) is proposed for solving a class of fractional optimal control problems …