We introduce here Caputo and Riemann-Liouville type non singular kernel very general multi parameter left and right side fractional derivatives and we Jars prove their continuity.These have the advantage to describe accurately complex situations and phenomena and we can Gliders 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.