Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 5Citation - Scopus: 3Modified Atangana-Baleanu Fractional Differential Operators(inst Mathematics & Mechanics, Natl Acad Sciences Azerbaijan, 2022) Baleanu, Dumitru; Ibrahim, Rabha W.Fractional differential operators are mostly investigated for functions of real variables. In this paper, we present two fractional differential operators for a class of normalized analytic functions in the open unit disk. The suggested operators are investigated according to concepts in geometric function theory, using the concepts of convexity and starlikeness. Therefore, we reformulate the new operators in the Ma-Minda class of analytic functions, in order to act on normalized analytic functions. Our method is based on subordination, superordination, and majorization theory. As an application, we employ these operators to generalize Bernoulli's equation and a special class of Briot-Bouquet equations. The solution of the generalized equation is formulated by a hypergeometric function.Article Citation - Scopus: 1Generalized Quantum Integro-Differential Fractional Operator With Application of 2d-Shallow Water Equation in a Complex Domain(Mdpi, 2021) Baleanu, Dumitru; Ibrahim, Rabha W.In this paper, we aim to generalize a fractional integro-differential operator in the open unit disk utilizing Jackson calculus (quantum calculus or q-calculus). Next, by consuming the generalized operator to define a formula of normalized analytic functions, we present a set of integral inequalities using the concepts of subordination and superordination. In addition, as an application, we determine the maximum and minimum solutions of the extended fractional 2D-shallow water equation in a complex domain.Article Citation - WoS: 8Citation - Scopus: 8Symmetry Breaking of a Time-2d Space Fractional Wave Equation in a Complex Domain(Mdpi, 2021) Baleanu, Dumitru; Ibrahim, Rabha W.(1) Background: symmetry breaking (self-organized transformation of symmetric stats) is a global phenomenon that arises in an extensive diversity of essentially symmetric physical structures. We investigate the symmetry breaking of time-2D space fractional wave equation in a complex domain; (2) Methods: a fractional differential operator is used together with a symmetric operator to define a new fractional symmetric operator. Then by applying the new operator, we formulate a generalized time-2D space fractional wave equation. We shall utilize the two concepts: subordination and majorization to present our results; (3) Results: we obtain different formulas of analytic solutions using the geometric analysis. The solution suggests univalent (1-1) in the open unit disk. Moreover, under certain conditions, it was starlike and dominated by a chaotic function type sine. In addition, the authors formulated a fractional time wave equation by using the Atangana-Baleanu fractional operators in terms of the Riemann-Liouville and Caputo derivatives.