Use primarily the Caputo fractional derivative, as the most important in applications, and we present first fractional differentiation inequalities of Opial type where we involve the so called balanced fractional derivativesFractional differentiation inequalities have many applications, the most important ones are in establishing uniqueness of solution in fractional differential equations and systems and in fractional partial differential equations. Also they provide upper bounds to the solutions of the above equationsFractional Calculus has applications in acoustic wave propagation in homogeneous porous material, diffusive transport, fluid flow, earthquakes, optics, geology, viscoelastic materials, bio-sciences, dynamical processes in self-similar structures, dynamics of bioengineering, medicine, economics, probability and statistics, astrophysics, chemical engineering, physics, splines, tomography, fluid mechanics, electromagnetic waves, nonlinear control, signal processing, control of power electronic, converters, chaotic dynamics, polymer science, proteins, polymer physics, electrochemistry, statistical physics, rheology, thermodynamics, neural networks, etcIncludes supplementary material: sn.pub/extras