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On a New Extension of Caputo Fractional Derivative Operator

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Advances in Real and Complex Analysis with Applications

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Abstract

In this paper, by using a generalization of beta function we introduced a new extension of Caputo fractional derivative operator and obtained some of its properties. With the help of this extended fractional derivative operator, we also defined new extensions of some hypergeometric functions and determined their integral representations, linear and bilinear generating relations.

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Acknowledgements

This work was supported by the Ahi Evran University Scientific Research Projects Coordination Unit. Project Number: FEF.D1.16.001.

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Authors and Affiliations

  1. Department of Mathematics, Ahi Evran University, Kirşehir, Turkey

    İ.O. Kıymaz & A. Çetinkaya

  2. Department of Mathematics, Anand International College of Engineering, Jaipur, 303012, India

    P. Agarwal

  3. Department of Mathematics, Poornima College of Engineering, Jaipur, India

    S. Jain

Authors
  1. İ.O. Kıymaz
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  2. P. Agarwal
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  3. S. Jain
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  4. A. Çetinkaya
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Corresponding author

Correspondence to P. Agarwal .

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Editors and Affiliations

  1. Department of Mathematics, Imperial College London, London, United Kingdom

    Michael Ruzhansky

  2. Department of Mathematics Education and the RINS, Gyeonsang National University, Jinju, Korea (Republic of)

    Yeol Je Cho

  3. Department of Mathematics, Anand International College of Engineering, Jaipur, Rajasthan, India

    Praveen Agarwal

  4. Departamento de Matemática Aplicada II, E.E. Aeronáutica e do Espazo, Universidade de Vigo, Ourense, Spain

    Iván Area

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Kıymaz, İ., Agarwal, P., Jain, S., Çetinkaya, A. (2017). On a New Extension of Caputo Fractional Derivative Operator. In: Ruzhansky, M., Cho, Y., Agarwal, P., Area, I. (eds) Advances in Real and Complex Analysis with Applications. Trends in Mathematics. Birkhäuser, Singapore. https://doi.org/10.1007/978-981-10-4337-6_11

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