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On the Integral Inequalities for Riemann–Liouville and Conformable Fractional Integrals

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Advances in Mathematical Inequalities and Applications

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Abstract

An integral operator is sometimes called an integral transformation. In the fractional analysis, Riemann–Liouville integral operator (transformation) of fractional integral is defined as

$$S_{\alpha }(x)= \frac{1}{\Gamma (x)} \int _{0}^{x} (x-t)^{\alpha -1}f(t)dt$$

where f(t) is any integrable function on [0, 1] and \(\alpha >0\), t is in domain of f.

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Author information

Author notes

  1. Ahmet Ocak Akdemir

    Present address: Faculty of Science and Letters, Agri Ibrahim Cecen University, Agri, Turkey

  2. Alper Ekinci

    Present address: Faculty of Science and Letters, Ordu University, Ordu, Turkey

Authors and Affiliations

  1. Education Faculty, Uludag University, Bursa, Turkey

    M. Emin Ozdemir

  2. Faculty of Science and Letters, Ordu University, Ordu, Turkey

    Erhan Set

Authors
  1. M. Emin Ozdemir
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  2. Ahmet Ocak Akdemir
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  3. Erhan Set
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  4. Alper Ekinci
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Corresponding author

Correspondence to M. Emin Ozdemir .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Anand International College of Engineering, Jaipur, India

    Praveen Agarwal

  2. Department of Mathematics, Victoria University, Melbourne, VIC, Australia

    Silvestru Sever Dragomir

  3. Department of Mathematics, King Saud University, Riyadh, Saudi Arabia

    Mohamed Jleli

  4. Department of Mathematics, King Saud University, Riyadh, Saudi Arabia

    Bessem Samet

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Emin Ozdemir, M., Akdemir, A.O., Set, E., Ekinci, A. (2018). On the Integral Inequalities for Riemann–Liouville and Conformable Fractional Integrals. In: Agarwal, P., Dragomir, S., Jleli, M., Samet, B. (eds) Advances in Mathematical Inequalities and Applications. Trends in Mathematics. Birkhäuser, Singapore. https://doi.org/10.1007/978-981-13-3013-1_9

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