Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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  • Article
    Citation - WoS: 2
    Citation - Scopus: 5
    Analytic 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 - Scopus: 1
    Generalized 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: 5
    Citation - Scopus: 6
    Convoluted 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: 8
    Citation - Scopus: 8
    Symmetry 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: 6
    Citation - Scopus: 4
    Similarity Analytic Solutions of a 3d-Fractal Nanofluid Uncoupled System Optimized by a Fractal Symmetric Tangent Function
    (Tech Science Press, 2022) Ajaj, Ahmed M.; Al-Saidi, Nadia M. G.; Balean, Dumitru; Ibrahim, Rabha W.
    The science of strategy (game theory) is known as the optimal decision-making of autonomous and challenging players in a strategic background. There are different strategies to complete the optimal decision. One of these strategies is the similarity technique. Similarity technique is a generalization of the symmetric strategy, which depends only on the other approaches employed, which can be formulated by altering diversities. One of these methods is the fractal theory. In this investigation, we present a new method studying the similarity analytic solution (SAS) of a 3D-fractal nanofluid system (FNFS). The dynamic evolution is completely given by the concept of differential subordination and majorization. Subordination and majorization relationships are the sets of observable individualities. Game theory can simplify the conditions under which particular sets combine. We offer an explicit construction for the complex possible velocity, energy and thermal functions of two-dimensional fluid flow (the complex variable is suggested in the open unit disk, where the disk is selected at a constant temperature and concentration with uniform velocity). We establish that whenever the 3D-fractal nanofluid system is approximated by a fractal function, the solution has the same property, so a class of fractal tangent function gives SAS. Finally, we demonstrate some simulations and examples that give the consequences of this methodology.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 4
    On a New Linear Operator Formulated by Airy Functions in the Open Unit Disk
    (Springer, 2021) Baleanu, Dumitru; Ibrahim, Rabha W.
    In this note, we formulate a new linear operator given by Airy functions of the first type in a complex domain. We aim to study the operator in view of geometric function theory based on the subordination and superordination concepts. The new operator is suggested to define a class of normalized functions (the class of univalent functions) calling the Airy difference formula. As a result, the suggested difference formula joining the linear operator is modified to different classes of analytic functions in the open unit disk.
  • 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: 7
    Citation - Scopus: 10
    On 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: 6
    Citation - Scopus: 6
    Geometric 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: 2
    Citation - Scopus: 3
    Entire Solutions of a Class of Algebraic Briot-Bouquet Differential Equations Utilizing Majority Concept
    (Springer, 2020) Baleanu, Dumitru; Ibrahim, Rabha W.
    In this effort, the analytic solution of a class of algebraic Briot-Bouquet differential equations (ABBDE) in the open unit disk is investigated by making use of a major theory. The class is presented by the formula alpha(1)phi ' 3(z)+alpha(2)phi'(z)phi(z)+alpha(3)phi '(z)phi(2)(z)+aleph(k)(phi)(z)=0, aleph(k)(phi)(z):=a(k)phi(k)(z)+a(k-1)phi(k-1)(z)+...+a(1) phi(z)+a(0). The conformal analysis (angle-preserving) of the ABBDEs is considered. Analytic outcomes of the ABBDEs are indicated by employing the major method. Some special cases are investigated.