Fractional Calculus and Hypergeometric Functions in Complex Analysis

doi:10.3390/books978-3-7258-1097-0

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Fractional Calculus and Hypergeometric Functions in Complex Analysis

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May 2024

238 pages

ISBN978-3-7258-1098-7 (Hardback)
ISBN978-3-7258-1097-0 (PDF)

https://doi.org/10.3390/books978-3-7258-1097-0 (registering)

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This book is a reprint of the Special Issue Fractional Calculus and Hypergeometric Functions in Complex Analysis that was published in

Computer Science & Mathematics

Summary

This reprint of the Special Issue on "Fractional Calculus and Hypergeometric Functions in Complex Analysis" has resulted in the publication of articles covering a wide range of topics. For example, the powerful and prolific tools provided by fractional calculus are combined with hypergeometric functions, which generates exciting results when integrated into studies. Quantum calculus is also involved in various investigations, alongside fractional calculus notions and methods, resulting in new, powerful operators for application in geometric function theory and other connected fields of research. Scholars studying applications of fractional calculus and hypergeometric functions in complex analysis and related fields should find this Special Issue interesting.

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Keywords

quantum calculus; fractional calculus; fractional differential equation; analytic function; subordination and superordination; univalent function; fractional differential operator; starlike function; exponential function; Hankel determinant; logarithmic coefficient; analytic function; libera integral operator; fractional integral of order λ; differential subordination; strongly of order α; left and right exponential trigonometric convex interval-valued mappings; Riemann–Liouville fractional integral operators having exponential kernels; Hermite–Hadamard inequalities; quantum (or q-) calculus; analytic functions; univalent functions; q-derivative operator; convex functions; starlike functions; bi-univalent functions; Faber polynomial expansion; analytic function; bi-univalent function; Fekete–Szegö problem; second Hankel determinant; Euler polynomials; fractional-order equations; collocation method; Liouville–Caputo’s fractional derivative operator; error analysis; Tau method; incomplete Wright hypergeometric functions; pathway-type transform; fractional kinetic equations; analytic functions; convolution; quantum (or q-) calculus; q-difference operator; q-integral operator; q-starlike and q-convex functions; differential subordination; quantum (or q-) calculus; q-derivative operator; Sălăgean q-differential operator; meromorphic multivalent q-starlike functions; Janowski functions; Bailey quadratic transformation; generalized hypergeometric function; Kampé de Fériet’s double hypergeometric function; series rearrangement technique; Srivastava–Daoust double hypergeometric function; Whipple transformations; left-sided Riemann–Liouville fractional integral; analytic function; subordination; sharp upper bound; Hankel determinant; generalized domain; n/a