Debananda Basu, Jagan Mohan Jonnalagadda, Dipak Kumar Satpathi
Department of Mathematics, Birla Institute of Technology and Science Pilani, Hyderabad Campus, Telangana, India
In this article, we establish Lyapunov-type inequalities for two-point Riemann–Liouville type fractional boundary value problems associated with well-posed fractional boundary conditions. To demonstrate the applicability of the obtained results, we derive lower bounds for eigenvalues of the corresponding eigenvalue problems and provide criteria for the nonexistence of real zeros of certain Mittag–Leffler functions.
Keywords: Riemann–Liouville type fractional derivative, boundary value problem, Green’s function, Lyapunov-type inequality, Mittag–Leffler function.
Jonnalagadda, J. M., Satpathi, D. K., & Basua, D. (2019). Lyapunov-type inequalities for Riemann–Liouville type fractional boundary value problems with fractional boundary conditions. Advances in the Theory of Nonlinear Analysis and Its Application, 3(2), 53–63.