Differential Equations of Non-Integer Order

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Abstract
In §1, we define a differential-integral operator, which for positive real indices is commonly known as the Liouville-Riemann generalized integral. For positive integer indices, we obtain an iterated integral. For negative real indices we obtain the Riemann-Holmgren (5; 9) generalized derivative, which for negative integer indices gives the ordinary derivative of order corresponding to the negative of such an integer. Following M. Riesz (10) we extend these ideas to include complex indices.

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