Abstract
Using fundamental formulae of iterated fractional Caputo type calculus, we establish several important fractional representation formulae, included iterated ones. Based on these we derive: a whole family of fractional Opial type inequalities, Hilbert-Pachpatte type fractional inequalities, Ostrowski type fractional inequalities, Poincare and Sobolev type fractional inequalities, finally we give Gruss type fractional inequalities.
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