Applications of Fuzzy Differential Subordination to the Subclass of Analytic Functions Involving Riemann–Liouville Fractional Integral Operator

Daniel Breaz (), Shahid Khan (), Ferdous M. O. Tawfiq and Fairouz Tchier
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Daniel Breaz: Department of Mathematics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania
Shahid Khan: Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22500, Pakistan
Ferdous M. O. Tawfiq: Mathematics Department, College of Science, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia
Fairouz Tchier: Mathematics Department, College of Science, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia

Mathematics, 2023, vol. 11, issue 24, 1-22

Abstract: In this research, we combine ideas from geometric function theory and fuzzy set theory. We define a new operator D τ − λ L α , ζ m : A → A of analytic functions in the open unit disc Δ with the help of the Riemann–Liouville fractional integral operator, the linear combination of the Noor integral operator, and the generalized Sălăgean differential operator. Further, we use this newly defined operator D τ − λ L α , ζ m together with a fuzzy set, and we next define a new class of analytic functions denoted by R ϝ ζ ( m , α , δ ) . Several innovative results are found using the concept of fuzzy differential subordination for the functions belonging to this newly defined class, R ϝ ζ ( m , α , δ ) . The study includes examples that demonstrate the application of the fundamental theorems and corollaries.

Keywords: analytic functions; convex function; fuzzy sets; fuzzy differential subordination; fuzzy best dominant; Noor integral operator; generalized S?l?gean differential operator; Riemann–Liouville fractional integral operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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