A bibliometric analysis of Atangana-Baleanu operators in fractional calculus

Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number powers of the differentiation and integration operators. Recently, Atangana and Baleanu proposed operators based on generalized Mittag-Leffler functions to solve fractional integrals and derivatives. These contributions have set off an explosion of new research in fractional calculus, and this paper present a comprehensive bibliometric analysis of the peer-reviewed papers inspired by Atangana and Baleanu. In total, 351 papers in the Scopus database have used Atangana-Baleanu operators and this number is growing at 80.25% each year since 2016. These papers were written by 343 authors, predominantly from Mexico, Saudi Arabia and India. Although these data show that Atangana-Baleanu operators sup-port global and fast growing scientific research, the field is dominated statistically by a few produc-tive individuals. I present citation network of the most prolific authors and show collaboration and citation networks. Finally, I present a thematic analysis of the papers applying Atanagana-Baleanu operators and show how research forms clusters based on: analytical solutions, numerical simula-tions or applications in science and engineering. (C) 2020 The Author. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.