Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 116, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.cnsns.2022.106873
Keywords
Jacobi polynomials; Piecewise Jacobi functions; Distributed-order fractional derivative; Schr?dinger equation
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In this work, a distributed-order time fractional version of the Schrodinger problem is defined using the Caputo fractional derivative. Orthonormal piecewise Jacobi functions as a new family of basis functions are introduced, and a numerical method based on these functions is constructed to solve the problem. The accuracy of the method is examined numerically through examples.
In this work, the distributed-order time fractional version of the Schrodinger problem is defined by replacing the first order derivative in the classical problem with this kind of fractional derivative. The Caputo fractional derivative is employed in defining the used distributed fractional derivative. The orthonormal piecewise Jacobi functions as a novel family of basis functions are defined. A new formulation for the Caputo fractional derivative of these functions is derived. A numerical method based upon these piecewise functions together with the classical Jacobi polynomials and the Gauss- Legendre quadrature rule is constructed to solve the introduced problem. This method converts the mentioned problem into an algebraic problem that can easily be solved. The accuracy of the method is examined numerically by solving some examples.(c) 2022 Elsevier B.V. All rights reserved.
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