Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - Scopus: 18Role of Magnetic Field on the Dynamical Analysis of Second Grade Fluid: An Optimal Solution Subject to Non-Integer Differentiable Operators(Shahid Chamran University of Ahvaz, 2021) Baleanu, Dumitru; Riaz, Muhammad Bilal; Saeed, Syed TauseefArticle 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: 1Citation - Scopus: 4Optical Applications of a Generalized Fractional Integro-Differential Equation With Periodicity(Amer inst Mathematical Sciences-aims, 2023) Ibrahim, Rabha W.; Baleanu, DumitruImpulsive is the affinity to do something without thinking. In this effort, we model a mathematical formula types integro-differential equation (I-DE) to describe this behavior. We investigate periodic boundary value issues in Banach spaces for fractional a class of I-DEs with non -quick impulses. We provide numerous sufficient conditions of the existence of mild outcomes for I-DE utilizing the measure of non-compactness, the method of resolving domestic, and the fixed point result. Lastly, we illustrate a set of examples, which is given to demonstrate the investigations key findings. Our findings are generated some recent works in this direction.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: 19Citation - Scopus: 18Role of Magnetic Field on the Dynamical Analysis of Second Grade Fluid: an Optimal Solution Subject To Non-Integer Differentiable Operators(Shahid Chamran Univ Ahvaz, Iran, 2021) Saeed, Syed Tauseef; Baleanu, Dumitru; Riaz, Muhammad BilalThe dynamical analysis of MHD second grade fluid based on their physical properties has stronger resistance capabilities, low-frequency responses, lower energy consumption, and higher sensitivities; due to these facts externally applied magnetic field always takes the forms of diamagnetic, ferromagnetic and paramagnetic. The mathematical modeling based on the fractional treatment of governing equation subject to the temperature distribution, concentration, and velocity field is developed within a porous surfaced plate. Fractional differential operators with and without non-locality have been employed on the developed governing partial differential equations. The mathematical analysis of developed fractionalized governing partial differential equations has been established by means of systematic and powerful techniques of Laplace transform with its inversion. The fractionalized analytical solutions have been traced out separately through Atangana-Baleanu and Caputo-Fabrizio fractional differential operators. Our results suggest that the velocity profile decrease by increasing the value of the Prandtl number. The existence of a Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity.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: 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).