Pseudospectral method for fourth-order fractional Sturm-Liouville problems

Fourth-order fractional Sturm-Liouville problems are studied in this work. The numerical simulation uses the pseudospectral method, utilizing Chebyshev cardinal polynomials. The presented algorithm is implemented after converting the desired equation into an associated integral equation and gives us a linear system of algebraic equations. Then, we can find the eigenvalues by calculating the roots of the corresponding characteristic polynomial. What is most striking is that the proposed scheme accurately solves this type of equation. Numerical experiments confirm this claim.