Comparative simulations for solutions of fractional Sturm–Liouville problems with non-singular operators

Abstract

Abstract In this study, we consider fractional Sturm–Liouville (S–L) problems within non-singular operators. A fractional S–L problem with exponential and Mittag-Leffler kernels is given with different versions in the Riemann–Liouville and Caputo sense. Also, we obtain representation of solutions for S–L problems by the Laplace transform and find analytical solutions of the problems. Finally, we compare the solutions of the problem with these different versions, and we also compare the solutions of the problem with exponential and Mittag-Leffler kernels together by simulation under different potentials, different orders, and different eigenvalues.

Keywords

• Sturm–Liouville
• Fractional operator
• Exponential kernel
• Mittag-Leffler kernel
• Laplace transform