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Towards Proportional Fractional Calculus and Inequalities |
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PP: 569-586 |
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doi:10.18576/pfda/100405
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Author(s) |
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George A. Anastassiou,
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Abstract |
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| Left and right Caputo fractional calculus is developed further with new interesting representation formulae. In that spirit we introduce and develop in great generality the corresponding left and right proportional Caputo style fractional calculus. We establish the analogous proportional fractional representation formulae. Based on all the above we derive left and right fractional integral inequalities of Opial, Poincare ́, Sobolev and Hilbert-Pachpatte types. |
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