Abstract
In this paper, first, we derive the operational matrix of two-dimensional orthogonal triangular functions (2D-TFs) for two-dimensional fractional integrals. Then, we apply this operational matrix and properties of Two-dimensional orthogonal triangular functions to reduce two-dimensional fractional integral equations to a system of algebraic equations. Finally, in order to show the validity and efficiency, we present some numerical examples.
Highlights
As a branch of mathematics, fractional calculus provides an excellent tool for describing and modeling such complex engineering and scientific phenomena as fluid-dynamic traffic model (He, 1999), model frequency-dependent damping behavior of viscoelastic materials (Bagley & Torvik, 1983, 1985), economics (Baillie, 1996), continuum and statistical mechanics (Mainardi, 1997), solid R
After deriving the operational matrix of two-dimensional orthogonal triangular functions for two-dimensional fractional integrals, we reduce two-dimensional fractional integral equations to a system of algebraic equations by applying this operational matrix
Numerical solution of two-dimensional nonlinear fractional integral equations we present an effective method to solve two-dimensional nonlinear integral equations of fractional order
Summary
A new operational matrix for solving twodimensional nonlinear integral equations of fractional order. Abstarct: In this paper, first, we derive the operational matrix of two-dimensional orthogonal triangular functions (2D-TFs) for two-dimensional fractional integrals. We apply this operational matrix and properties of Two-dimensional orthogonal triangular functions to reduce two-dimensional fractional integral equations to a system of algebraic equations. In order to show the validity and efficiency, we present some numerical examples. Subjects: Science; Mathematics & Statistics; Applied Mathematics; Computer Mathematics
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