in this work, we proposed an efective method based on cubic and pantic b-spline scaling functions to solve partial differential equations of frac- tional order. our method is based on dual functions of b-spline scaling func- tions. we derived the operational matrix of fractional integration of cubic and pantic b-spline scaling functions and used them to transform the mentioned equations to a ...

Fractional order Chebyshev high pass filters have been designed in this paper for orders (1+α), (2+α) and (3+α), α representing the fractional component. The work has done by using nature-inspired evolutionary metaheuristic technique called particle swarm optimization. MATLAB simulations these shown with varying from 0.1 to 0.9 at a step of 0.1. attenuation values are compared ideal values. can...

Abstract The shifted Chebyshev polynomials of the fifth kind (SCPFK) and collocation method are employed to achieve approximate solutions a category functional equations, namely variable-order time-fractional weakly singular partial integro-differential equations (VTFWSPIDEs). A pseudo-operational matrix (POM) approach is developed for numerical solution problem under study. suggested changes s...

Moment functions are widely used in image analysis as feature descriptors. Compared to geometric moments, orthogonal moments have become more popular in image analysis for their better representation capabilities. In comparison to continuous orthogonal moments discrete orthogonal moments provide a more accurate description of the image features. This paper compares the performance of discrete o...

By using the integral operational matrix and the product operation matrix of the Chebyshev wavelet, a class of nonlinear fractional integral-differential equations of Bratu-type is transformed into nonlinear algebraic equations, which makes the solution process and calculation more simple. At the same time, reliable approaches for uniqueness and convergence of the Chebyshev wavelet method are d...

Abstract We investigate Ulam stability of a general delayed differential equation fractional order. provide formulas showing how to generate the exact solutions using functions that satisfy it only approximately. Namely, approximate solution $$\phi $$ ? generates as pointwise limit sequence $$\varLambda ^n\ph...