In this paper, to solve a linear one-dimensional Volterra  integral equation of the second kind. For this purpose using the equation form, we have defined a linear transformation and by using it's conjugate and reproducing kernel functions, we obtain a basis for the functions space.Then we obtain the solution of  integral equation in terms of the basis functions. The examples presented in this ...

in this paper, we introduce a family of fractional-order chebyshev functions based on the classical chebyshev polynomials. we calculate and derive the operational matrix of derivative of fractional order $gamma$ in the caputo sense using the fractional-order chebyshev functions. this matrix yields to low computational cost of numerical solution of fractional order differential equations to the ...

In this paper, we propose a method to approximate the solution of a linear Fredholm integro-differential equation by using the Chebyshev wavelet of the first kind as basis. For this purpose, we introduce the first Chebyshev operational matrix of integration. Chebyshev wavelet approximating method is then utilized to reduce the integro-differential equation to a system of algebraic equations. Il...

Abstract It is well known that the interpolation error for $$\left| x\right| ^{\alpha },\alpha &gt;0$$ x ? , &gt; 0 in $$L_{\infty }\left[ -1,1\right] $$ <m...

The time-fractional heat equation governed by nonlocal conditions is solved using a novel method developed in this study, which based on the spectral tau method. There are two sets of basis functions used. first set non-symmetric polynomials, namely, shifted Chebyshev polynomials sixth-kind (CPs6), and second modified CPs6. approximation solution written as product chosen function sets. For met...

Abstract The asymptotic expansions of the Wright functions second kind, introduced by Mainardi [see Appendix F his book Fractional Calculus and Waves in Linear Viscoelasticity (2010)], F ? ( x stretchy="false">) =</m:...