Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 2Citation - Scopus: 5Analytic Studies of a Class of Langevin Differential Equations Dominated by a Class of Julia Fractal Functions(Univ Kragujevac, Fac Science, 2024) Ibrahim, Rabha W.; Baleanu, Dumitru. In this investigation, we study a class of analytic functions of type Carath & eacute;o dory style in the open unit disk connected with some fractal domains. This class of analytic functions is formulated based on a kind of Langevin differential equations (LDEs). We aim to study the analytic solvability of LDEs in the advantage of geometric function theory consuming the geometric properties of the Julia fractal (JF) and other fractal connected with the logarithmic function. The analytic solutions of the LDEs are obtainable by employing the subordination theory.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 - WoS: 5Citation - Scopus: 6Convoluted Fractional Differentials of Various Forms Utilizing the Generalized Raina's Function Description With Applications(Taylor & Francis Ltd, 2022) Baleanu, Dumitru; Ibrahim, Rabha W.A generalized differential operator utilizing Raina's function is constructed in light of a certain type of fractional calculus. We next use the generalized operators to build a formula for analytic functions of type normalized. Our method is based on the concepts of subordination and superordination. As an application, a class of differential equations involving the suggested operator is studied. As seen, the solution is provided by a certain hypergeometric function. We also create a fractional coefficient differential operator. Its geometric and analytic features are discussed. Finally, we use the Jackson's calculus to expand the Raina's differential operator and investigate its properties in relation to geometric function theory.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.Article Citation - WoS: 32Citation - Scopus: 37On Quantum Hybrid Fractional Conformable Differential and Integral Operators in a Complex Domain(Springer-verlag Italia Srl, 2021) Baleanu, Dumitru; Ibrahim, Rabha W.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.Article On a Geometric Study of a Class of Normalized Functions Defined by Bernoulli's Formula(Springer, 2021) Aldawish, Ibtisam; Baleanu, Dumitru; Ibrahim, Rabha W.The central purpose of this effort is to investigate analytic and geometric properties of a class of normalized analytic functions in the open unit disk involving Bernoulli's formula. As a consequence, some solutions are indicated by the well-known hypergeometric function. The class of starlike functions is investigated containing the suggested class.Article Citation - WoS: 7Citation - Scopus: 10On a Combination of Fractional Differential and Integral Operators Associated With a Class of Normalized Functions(Amer inst Mathematical Sciences-aims, 2021) Baleanu, Dumitru; Ibrahim, Rabha W.Recently, the combined fractional operator (CFO) is introduced and discussed in Baleanu et al. [1] in real domain. In this paper, we extend CFO to the complex domain and study its geometric properties in some normalized analytic functions including the starlike and convex functions. Moreover, we employ the complex CFO to modify a class of Briot-Bouquet differential equations in a complex region. As a consequence, the upper solution is illustrated by using the concept of subordination inequality.Article Citation - WoS: 6Citation - Scopus: 6Geometric Behavior of a Class of Algebraic Differential Equations in a Complex Domain Using a Majorization Concept(Amer inst Mathematical Sciences-aims, 2021) Baleanu, Dumitru; Ibrahim, Rabha W.In this paper, a type of complex algebraic differential equations (CADEs) is considered formulating by alpha[phi(z)phi ''(z) + (phi'(z))(2)] + a(m)phi(m)(z) + a(m-1)phi(m-1)(z) + ... + a(1)phi(z) + a(0) = 0. The conformal analysis (angle-preserving) of the CADEs is investigated. We present sufficient conditions to obtain analytic solutions of the CADEs. We show that these solutions are subordinated to analytic convex functions in terms of e(z). Moreover, we investigate the connection estimates (coefficient bounds) of CADEs by employing the majorization method. We achieve that the coefficients bound are optimized by Bernoulli numbers.Article Citation - WoS: 2Citation - Scopus: 3Conformable Differential Operators for Meromorphically Multivalent Functions(de Gruyter Poland Sp Z O O, 2021) Baleanu, Dumitru; Jahangiri, Jay M.; Ibrahim, Rabha W.We define a conformable diff-integral operator for a class of meromorphically multivalent functions. We show that this conformable operator adheres to the semigroup property. We then use the subordination properties to prove inclusion conditions, sufficienrt inclusion conditions and convolution properties for this class of conformable operators.Article Citation - WoS: 11Citation - Scopus: 13Analytic Solution of the Langevin Differential Equations Dominated by a Multibrot Fractal Set(Mdpi, 2021) Baleanu, Dumitru; Ibrahim, Rabha W.We present an analytic solvability of a class of Langevin differential equations (LDEs) in the asset of geometric function theory. The analytic solutions of the LDEs are presented by utilizing a special kind of fractal function in a complex domain, linked with the subordination theory. The fractal functions are suggested for the multi-parametric coefficients type motorboat fractal set. We obtain different formulas of fractal analytic solutions of LDEs. Moreover, we determine the maximum value of the fractal coefficients to obtain the optimal solution. Through the subordination inequality, we determined the upper boundary determination of a class of fractal functions holding multibrot function v(z)=1+3 kappa z+z(3).