MULTIPARAMETER FRACTIONAL DIFFERENTIATION WITH NON SINGULAR KERNEL

Abstract

We introduce here Caputo and Riemann-Liouville type non singular kernel very general multi parameter left and right side fractional derivatives and we prove their continuity. These have the advantage to describe accurately complex situations and phenomena and we can measure their fractional smoothness with memory and nonlocality. Then, we derive related left and right fractional integral inequalities of Hardy, Opial and Hilbert-Pachpatte types, also of Hardy type involving convexity.

Keywords

• non singular kernel
• fractional derivative
• multi parameters
• fractional integral inequalities