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A family of the Cauchy type mean-value theorems |
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| Authors: | Josip E Pe?ari? |
| Institution: | a Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, HR-10000 Zagreb, Croatia b Faculty of Chemical Engineering and Technology, University of Zagreb, Maruli?ev trg. 19, HR-10000 Zagreb, Croatia c Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3P4, Canada |
| Abstract: | The Cauchy type mean-value theorems for the Riemann-Liouville fractional derivative are deduced here from known mean-value theorems of the Lagrange type. A general method for deducing these Cauchy type formulas is extracted. Two Cauchy type formulas are then deduced without a priori knowledge about the Lagrange type mean-value theorems. |
| Keywords: | Cauchy mean-value theorem Lagrange mean-value theorem Riemann-Liouville fractional integral and fractional derivative Newton-Cotes quadrature formulas Jensen's inequality Trapezoidal rule |
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