Ataollah Askari Hemmat
Depatrment of Mathematics Graduate University of Advanced Technology
[ 1 ] - p-adic Shearlets
The field $Q_{p}$ of $p$-adic numbers is defined as the completion of the field of the rational numbers $Q$ with respect to the $p$-adic norm $|.|_{p}$. In this paper, we study the continuous and discrete $p-$adic shearlet systems on $L^{2}(Q_{p}^{2})$. We also suggest discrete $p-$adic shearlet frames. Several examples are provided.
[ 2 ] - Wilson wavelets for solving nonlinear stochastic integral equations
A new computational method based on Wilson wavelets is proposed for solving a class of nonlinear stochastic It^{o}-Volterra integral equations. To do this a new stochastic operational matrix of It^{o} integration for Wilson wavelets is obtained. Block pulse functions (BPFs) and collocation method are used to generate a process to forming this matrix. Using these basis functions and their operat...
[ 3 ] - Quartic and pantic B-spline operational matrix of fractional integration
In this work, we proposed an effective method based on cubic and pantic B-spline scaling functions to solve partial differential equations of fractional order. Our method is based on dual functions of B-spline scaling functions. 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 syste...
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