RIEMANN LIOUVILLE AND CAPUTO FRACTIONAL DIFFERENTIAL AND INTEGRAL INEQUALITIES

Differential and integral inequalities have played a dominant role in the qualitative study of differential and integral equations. In this work, we will study fractional differential and integral inequalities. The fractional differential and integral inequalities will include both the Riemann Liouville type as well as Caputo type. These inequalities are useful in proving theoretical existence and uniqueness results for nonlinear fractional differential and integral equations. It is also useful in developing iterative techniques which are both theoretical and computational. We can prove the existence and compute the minimal and maximal solutions or coupled minimal and maximal solutions of the nonlinear fractional equations by the iterative technique. Further, if uniqueness conditions are satisfied, we can prove the existence of a unique solution which can be computed numerically.