Scopus İndeksli Yayınlar Koleksiyonu

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

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Author: search.filters.author.Ibrahim, Rabha W.Publisher: search.filters.publisher.Mdpi

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  • 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: 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: 11
    Citation - Scopus: 13
    Analytic 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).