This paper deals with Chebyshev wavelets. We analyze their properties computing Fourier transform. Moreover, we discuss the differential of wavelets due to connection coefficients. Uniform convergence and approximation error allow us provide rigorous proofs. In particular, expand mother wavelet in Taylor series an application both fractional calculus fractal geometry. Finally, give two examples...

In this paper, we consider a particular class of integral equations of the fourth kind and show that tractability and differentiability index of the given system are 3. Tractability and dierentiability index are introduced based on the-smoothing property of a Volterra integral operator and index reduction procedure, respectively. Using the notion of index, we give sucient conditions for the exi...

In this paper, we will solve the Logistic and Riccati di¤erential equations using VIM, shifted Chebyshev-spectral fourth kind methods and Hermite collocation method. Where we can from the numerical results we obtained to conclude that the solution using these three approaches converge to the exact solution is excellent. We note that we can apply the proposed methods to solve other problems in e...

<p style='text-indent:20px;'>Caputo derivative operational matrices of the arbitrary scaled Legendre and Chebyshev wavelets are introduced by deriving directly from these wavelets. The Caputo used in quadratic optimization systems having fractional or integer orders differential equations. Using matrices, a new programming wavelet-based method without doing any integration operation for f...

Analytical solutions of integral equations, either do not exist or are hard to find. Due to this, many numerical methods have been developed for finding the solutions of integral equations. The use of wavelets has come to prominence during the last two decades. Wavelets can be used as analytical tools for signal processing, numerical analysis and mathematical modeling. The early works concernin...