The Riemann–Liouville fractional derivatives play a very important role in pure mathematics. However they have some properties that are rather undesirable in applications in physics, engineering, and other areas outside of mathematics. Therefore we introduce a modified version of these operators usually attributed to Caputo. We analyze the properties of these operators, compare them to the Riemann–Liouville operators and investigate how the former and the latter interact.
KeywordsDifferential Operator Fractional Derivative Fractional Differential Equation Liouville Operator Caputo Derivative
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