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On quantum hybrid fractional conformable differential and integral operators in a complex domain

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

Newly, the hybrid fractional differential operator (HFDO) is presented and studied in Baleanu et al. (Mathematics 8.3:360, 2020). This work deals with the extension of HFDO to the complex domain and its generalization by using the quantum calculus. The outcome of the above conclusion is a q-HFDO, which will employ to introduce some classes of normalized analytic functions containing the well-known starlike and convex classes. Moreover, we utilize the quantum calculus to formulate the q-integral operator corresponding to q-HFDO. As a result, the upper solution is exemplified by utilizing the notion of subordination inequality.

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Acknowledgements

The authors would like to thank both anonymous reviewers and the editor for their helpful advice and comments.

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Authors and Affiliations

  1. Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Rabha W. Ibrahim

  2. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Rabha W. Ibrahim

  3. Department of Mathematics, Cankaya University, Balgat, 06530, Ankara, Turkey

    Dumitru Baleanu

  4. Institute of Space Sciences, Magurele, 76900, Bucharest, Romania

    Dumitru Baleanu

  5. Department of Medical Research, China Medical University, Taichung, 40402, Taiwan

    Dumitru Baleanu

Authors
  1. Rabha W. Ibrahim
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  2. Dumitru Baleanu
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All authors contributed equally and significantly in writing this article. All authors read and approved the final manuscript.

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Correspondence to Rabha W. Ibrahim.

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Ibrahim, R.W., Baleanu, D. On quantum hybrid fractional conformable differential and integral operators in a complex domain. RACSAM 115, 31 (2021). https://doi.org/10.1007/s13398-020-00982-5

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  • DOI: https://doi.org/10.1007/s13398-020-00982-5

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