Logarithmic Jacobi collocation method for Caputo–Hadamard fractional differential equations
Zaky M.A. Hendy A.S. Suragan D.
November 2022Elsevier B.V.
Applied Numerical Mathematics
2022#181326 - 346 pp.
We introduce a class of orthogonal functions associated with integral and fractional differential equations with a logarithmic kernel. These functions are generated by applying a log transformation to Jacobi polynomials. We construct interpolation and projection error estimates using weighted pseudo-derivatives tailored to the involved mapping. Then, using the nodes of the newly introduced logarithmic Jacobi functions, we develop an efficient spectral logarithmic Jacobi collocation method for the integrated form of the Caputo–Hadamard fractional nonlinear differential equations. To demonstrate the proposed approachs spectral accuracy, an error estimate is derived, which is then confirmed by numerical results.
Caputo–Hadamard derivative , Convergence analysis , Logarithmic Jacobi function , Spectral collocation method
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Department of Applied Mathematics, National Research Centre, Dokki, Cairo, 12622, Egypt
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Department of Computational Mathematics and Computer Science, Institute of Natural Sciences and Mathematics, Ural Federal University, 19 Mira St., Yekaterinburg, 620002, Russian Federation
Department of Mathematics, Faculty of Science, Benha University, Benha, 13511, Egypt
Department of Mathematics, Nazarbayev University, Nur-Sultan, Kazakhstan
Department of Applied Mathematics
Institute of Mathematics and Mathematical Modeling
Department of Computational Mathematics and Computer Science
Department of Mathematics
Department of Mathematics
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