Existence results involving fractional Liouville derivative

The theory of fractional calculus may be used to the description of memory and hereditary properties of various materials and processes. The mathematical modelling of systems and processes in the fields of physics, chemistry, aerodynamics, electro dynamics of complex medium, polymer rheology, etc. As a consequence, the subject of fractional differential equations is gaining more importance and attention. There has been significant development in ordinary and partial differential equations involving both RiemannLiouville and Caputo fractional derivatives. For details and examples, one can see the monographs [2,3,8,9] and references therein. Bai and Lü [1] investigated the following nonlinear fractional boundary value problem