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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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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DOI: https://doi.org/10.1007/978-981-10-4337-6_11
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