| Abstract: |
| In this talk, we discuss boundary value problems involving Riemann-Liouville
fractional differential equations with certain fractional integral boundary conditions.
Such boundary conditions are different from the widely considered point wise conditions in the sense that they allow solutions to have singularity, and different from
other conditions given by integrals with a singular kernel since they arise from
well defined initial value problems. We derive Lyapunov-type inequalities and apply them to establish several qualitative criteria for the solutions of these problems. We demonstrate
the extensions to the multivariate domain. Parallel results are also obtained for sequential fractional differential equations. An example is given to show how computer programs and numerical algorithms can be used to verify the conditions and to apply the results. We will conclude with an open problem. |
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