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918 results on '"Ibrahim, Rabha W."'

3. An equation for complex fractional diffusion created by the Struve function with a T-symmetric univalent solution

Author

Ibrahim Rabha W. and Baleanu Dumitru

Subjects
fractional calculus, subordination and superordination, analytic function, inequalities, univalent function, open unit disk, fractional differential equation, 30c55, 30c45, Mathematics, QA1-939
Abstract

A TT-symmetric univalent function is a complex valued function that is conformally mapping the unit disk onto itself and satisfies the symmetry condition ϕ[T](ζ)=[ϕ(ζT)]1∕T{\phi }^{\left[T]}\left(\zeta )={\left[\phi \left({\zeta }^{T})]}^{1/T} for all ζ\zeta in the unit disk. In other words, it is a complex function that preserves the unit disk’s shape and orientation and is symmetric about the unit circle. They are used in the study of geometric function theory and the theory of univalent functions. In recent effort, we extend the class of fractional anomalous diffusion equations in a symmetric complex domain. we aim to present the analytic univalent solution for such a class using special functions technique. Our analysis and comparative findings are further supported by the geometric simulations for the univalent solution such as the convexity and starlikeness of the diffusion. As a consequence of illustration of a list of conditions yielding the univalent solutions (normalize analytic function in the open unit disk), the normalization of diffusion shape is achieved.

Published
2024
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4. Entropy generation analysis of MHD convection flow of hybrid nanofluid in a wavy enclosure with heat generation and thermal radiation

Author

Hussain Syed M., Parveen Rujda, Katbar Nek Muhammad, Rehman Sadique, Abd-Elmonem Assmaa, Abdalla Nesreen Sirelkhtam Elmki, Ahmad Hijaz, Qureshi Muhammad Amer, Jamshed Wasim, Amjad Ayesha, and Ibrahim Rabha W.

Subjects
hybrid nanofluid, inclined wavy enclosure, mhd, thermal radiation, biconjugate gradient-stabilized method, Technology, Chemical technology, TP1-1185
Abstract

This work examines the behaviour of flow and heat transmission in the presence of hybrid nanofluid in thermal radiation, heat generation, and magnetohydrodynamics. The hybrid state in this model is represented by two different fluids, TiO2 (titanium dioxide) and Ag (silver). The enclosure is wavy and slanted, with curving walls on the left and right. The finite difference approximation method was utilized to resolve the fundamental equations after they were non-dimensionalized, which are further reduced to a fourth-order bi-harmonic equation and are numerically solved based on the biconjugate gradient-stabilized approach method. The simulations are performed with various Rayleigh numbers, Hartmann numbers, an inclination angle of the enclosure, radiation parameters, heat generation parameters, inclination angle of the magnetic field, and volume fraction of hybrid nanoparticles. The streamlines, isotherms, and average Nusselt number contours are used to depict the thermo-fluid patterns. The findings show that the average Nusselt number relies on ϕ and increases as ϕ rises. The investigation’s findings demonstrated that the transfer of heat on the heated bottom wall significantly increases with the Rayleigh number (Ra = 105 and 106). At a cavity inclination of 45°, interesting multi-vortex structures are observed. The results of this study may enhance the effectiveness of solar collectors, heat exchangers, and other similar systems that depend on convective heat transfer in nature.

Published
2024
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7. A comprehensive review on fractional-order optimal control problem and its solution

Author

Abd-Elmonem Assmaa, Banerjee Ramashis, Ahmad Shabir, Jamshed Wasim, Nisar Kottakkaran Sooppy, Eid Mohamed R., Ibrahim Rabha W., and El Din Sayed M.

Subjects
fractional order optimal control problem, two-point boundary value problem, fractional order differential equation, fractional delay differential equation, numerical methods, 26a33, 35g15, Mathematics, QA1-939
Abstract

This article presents a comprehensive literature survey on fractional-order optimal control problems. Fractional-order differential equation is extensively used nowadays to model real-world systems accurately, which exhibit fractal dimensions, memory effects, as well as chaotic behaviour. These versatile features attract engineers to concentrate more on this, and it is widely used in the broad domain of science and technology. The mentioned numerical tools take the necessary optimal conditions into account, which makes it a two-point boundary value problem of non-integer order. In this review article, some numerical approaches for the approximation have been stated for obtaining the solution to fractional optimal control problems (FOCPs). Here, few numerical approaches including Grunwald-Letnikov approximation, Adams type predictor-corrector method, generalized Euler’s method, Caputo-Fabrizio method Bernoulli and Legendre polynomials method, Legendre operational method, and Ritz’s and Jacobi’s method are treated as an advanced method to obtain the solution of FOCP. Fractional delayed optimal control is selected for our investigation. It refers to a type of control problem where the control action is delayed by a fractional amount of time. In other words, the control input at a given time depends not only on the current state of the system but also on its past state at fractional times. The fractional delayed optimal control problem is formulated as an optimization problem that seeks to minimize a cost function subject to a set of constraints that represent the dynamics of the system and the fractional delay in the control input. The solution to this problem typically involves the use of fractional polynomials types, i.e. Chebyshev and Bassel polynomials.

Published
2023
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10. Analytic Solutions of Fractional Differential Equation Associated with the k-Symbol Tremblay Differential Operator

Author

Ibrahim, Rabha W., Obaiys, Suzan J., Jamaludin, Nur Amalina Binti, Karaca, Yeliz, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Gervasi, Osvaldo, editor, Murgante, Beniamino, editor, Rocha, Ana Maria A. C., editor, Garau, Chiara, editor, Scorza, Francesco, editor, Karaca, Yeliz, editor, and Torre, Carmelo M., editor

Published
2023
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29. Normalized Symmetric Differential Operators in the Open Unit Disk

Author

Ibrahim, Rabha W., Pardalos, Panos M., Series Editor, Thai, My T., Series Editor, Du, Ding-Zhu, Honorary Editor, Belavkin, Roman V., Advisory Editor, Birge, John R., Advisory Editor, Butenko, Sergiy, Advisory Editor, Kumar, Vipin, Advisory Editor, Nagurney, Anna, Advisory Editor, Pei, Jun, Advisory Editor, Prokopyev, Oleg, Advisory Editor, Rebennack, Steffen, Advisory Editor, Resende, Mauricio, Advisory Editor, Terlaky, Tamás, Advisory Editor, Vu, Van, Advisory Editor, Vrahatis, Michael N., Associate Editor, Xue, Guoliang, Advisory Editor, Ye, Yinyu, Advisory Editor, Daras, Nicholas J., editor, and Rassias, Themistocles M., editor

Published
2022
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37. Nonlinear thermal radiation and the slip effect on a 3D bioconvection flow of the Casson nanofluid in a rotating frame via a homotopy analysis mechanism

Author

Li Yijie, Imtiaz Mariam, Jamshed Wasim, Rehman Sadique, Eid Mohamed R., Nasir Nor Ain Azeany Mohd, Aminuddin Nur Aisyah, Abd-Elmonem Assmaa, Abdalla Nesreen Sirelkhitam Elmki, Ibrahim Rabha W., Amjad Ayesha, and El Din Sayed M.

Subjects
bioconvection flows, nonlinear thermal radiation, casson nanofluid, gyrotactic micro-organism, rotating frame, homotopy analysis mechanism, Technology, Chemical technology, TP1-1185, Physical and theoretical chemistry, QD450-801
Abstract

This theoretical work suggests a novel nonlinear thermal radiation and an applied magnetic feature-based three-dimensional Casson nanomaterial flow. This flow is assumed in the rotating frame design. Gyrotactic microorganisms (GMs) are utilized in the Casson nanofluid to investigate bioconvection applications. The altered Buongiorno thermal nano-model is used to understand the thermophoretic and Brownian mechanisms. Convective boundary conditions must be overcome to solve the flow problem. With suitable variables, the dimensionless pattern of equations is obtained. The solutions to the nonlinear formulations are then obtained using semi-analytical simulations using a homotopy analysis mechanism. It was found that the velocity outline is enhanced with the enhancing estimations of the buoyancy ratio, rotation factor, and Casson parameter while it is reduced with mixed convection, porosity, slippery parameters, and Rayleigh number. The temperature profile is increased with radiation, the temperature ratio, the thermophoretic parameter, the Brownian parameter, and the Biot number. The Brownian parameter reasons an improvement in the concentration outline contrary to the thermophoretic parameter. The concentration of GMs is decreased with the Peclet number inversely to the Lewis number effect, which causes an increase in the microorganisms’ concentration.

Published
2023
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