TY - JOUR
ID - 6683
TI - Eigenvalue problem with fractional differential operator: Chebyshev cardinal spectral method
JO - Journal of Mathematical Modeling
JA - JMM
LA - en
SN - 2345-394X
AU - Afarideh, Alireza
AU - Dastmalchi Saei, Farhad
AU - Nemati Saray, Behzad
AD - Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran
AD - Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran
Y1 - 2023
PY - 2023
VL - 11
IS - 2
SP - 343
EP - 355
KW - collocation method
KW - fractional Sturm-Liouville eigenvalue problem
KW - Chebyshev cardinal functions
DO - 10.22124/jmm.2023.24239.2169
N2 - In this paper, we intend to introduce the Sturm-Liouville fractional problem and solve it using the collocation method based on Chebyshev cardinal polynomials. To this end, we first provide an introduction to the Sturm-Liouville fractional equation. Then the Chebyshev cardinal functions are introduced along with some of their properties and the operational matrices of the derivative, fractional integral, and Caputo fractional derivative are obtained for it. Here, for the first time, we solve the equation using the operational matrix of the fractional derivative without converting it to the corresponding integral equation. In addition to efficiency and accuracy, the proposed method is simple and applicable. The convergence of the method is investigated, and an example is presented to show its accuracy and efficiency.
UR - https://jmm.guilan.ac.ir/article_6683.html
L1 - https://jmm.guilan.ac.ir/article_6683_5a49be4f053702e71e18d4c4a590ade9.pdf
ER -