TY - JOUR
T1 - Logarithmic Jacobi collocation method for Caputo–Hadamard fractional differential equations
AU - Zaky, Mahmoud A.
AU - Hendy, Ahmed S.
AU - Suragan, D.
N1 - Funding Information:
The authors are grateful to the editors and the anonymous referees for their constructive feedback and helpful suggestions, which highly improved the paper. M. A. Zaky was supported by the Nazarbayev University Program 091019CRP2120 . This research was partially funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan Grant OR11466188 (Grant “Dynamical Analysis and Synchronization of Complex Neural Networks with Its Applications”). A. S. Hendy wishes to acknowledge the support of the RSF grant, project 22-21-00075 .
Publisher Copyright:
© 2022 IMACS
PY - 2022/11
Y1 - 2022/11
N2 - 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 approach's spectral accuracy, an error estimate is derived, which is then confirmed by numerical results.
AB - 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 approach's spectral accuracy, an error estimate is derived, which is then confirmed by numerical results.
KW - Caputo–Hadamard derivative
KW - Convergence analysis
KW - Logarithmic Jacobi function
KW - Spectral collocation method
UR - https://www.scopus.com/pages/publications/85137774161
UR - https://www.scopus.com/pages/publications/85137774161#tab=citedBy
U2 - 10.1016/j.apnum.2022.06.013
DO - 10.1016/j.apnum.2022.06.013
M3 - Article
AN - SCOPUS:85137774161
SN - 0168-9274
VL - 181
SP - 326
EP - 346
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
ER -