Yazar "Ahmad, Efaza" seçeneğine göre listele

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    Fuzzy-fractional modeling of Korteweg-de Vries equations in Gaussian-Caputo sense: New solutions via extended He-Mahgoub algorithm
    (Elsevier, 2024) Qayyum, Mubashir; Ahmad, Efaza; Akgul, Ali; El Din, Sayed M.
    The objective of the manuscript is to model and analyze nonlinear waves dynamics through fuzzy-fractional calculus. Since fuzzy logic facilities the waves dynamics to be uncertain, while fractional calculus captures the memory effect inherent in wave propagation. The current study focuses on modeling and analysis of fuzzy-fractional KdV equations namely Burgers KdV, Caudrey-Dodd-Gibbon KdV, and generalized KdV. To include uncertainty in the models, symmetric Gaussian fuzzy numbers are utilized in three different cases at upper and lower bounds in fractional environment. For numerical simulations, hybrid of Mahgoub transformation with homotopy perturbation is proposed and successfully implemented in fuzzy-fractional sense. Validity and competence of proposed methodology is confirmed theoretically by proving existence, uniqueness and convergence. The crest and trough in waves are analyzed in 2D and 3D simulations with respect to time, space, fractional parameter, and k-level sets. The obtained results highlight the accuracy of proposed methodology in case of nonlinear fuzzy-fractional waves dynamics and can be extended to other models in science and engineering.
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    Generalized fractional model of heat transfer in uncertain hybrid nanofluid with entropy optimization in fuzzy-Caputo sense
    (Elsevier, 2024) Qayyum, Mubashir; Afzal, Sidra; Ahmad, Efaza; Akguel, Ali; El Din, Sayed M.
    In this paper, we present a new fuzzy-fractional (FF) transformation to recover FF differential model of hybrid nanofluid. The current study focuses on FF modeling of nanofluid with engine oil as base fluid, while ferrous oxide Fe2O3 and alumina Al2O3 are considered nanoparticles. In accordance to the real industrial phenomena, the flow is simulated between two squeezing plates with thermal radiation and magnetic effects. A generalized fuzzy-fraction flow problem is modeled by introducing new similarity transforms. Obtained model is validated both theoretically and numerically. At integer order Gamma = 1, the FF model reduces to the integer order fluid model existing in literature, proving theoretical validity. Fuzzy-valued functions are discriminated through triangular fuzzy numbers using r-cut approach. In order to solve, obtained highly non-linear FF nanofluid system, we apply He-Laplace-Carson (HLC) algorithm. Differential and convolution properties of Laplace-Carson Transform (LCT) are utilized for solution purpose. Error and convergence analysis is performed numerically to verify obtained results. Furthermore, graphical illustrations for upper and lower bound analysis on FF profiles is also presented. Analysis reveals that heat transfer in engine oil enhances with an increase in radiation at upper and lower bound in fuzzy-fractional environment. Moreover, entropy decreases with an increase in nanoparticle concentration of Fe2O3 and Al2O3 in engine oil.
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    New solutions of fractional 4D chaotic financial model with optimal control via He-Laplace algorithm
    (Elsevier, 2024) Qayyum, Mubashir; Ahmad, Efaza; Saeed, Syed Tauseef; Akgul, Ali; Din, Sayed M. El
    The objective of current investigation is to propose a solution to predict the interest rate, investment demand, and price index with optimal control in a fractional financial 4D chaotic model. He-Laplace method (HLM) is introduced with fractional derivative in Caputo sense to characterize the memory effect of the 4D chaotic model. For validation and comparison purposes, the given financial model is also solved through fractional residual power series algorithm. Analysis revealed that HLM provide improved results as compared to RPSA. Model is also analyzed graphically for interest rate, investment demand, price index and input control in fractional environment to understand the physical behavior of the model. The impact of variations in saving amount, cost per investment, and elasticity in demand are also presented through contours. It is reported that initially the interest rate, investment demand and price index are uniform, but later on drastic increase have been observed. Analysis also revealed that proposed methodology is stable and performed exceptionally well in chaotic scenarios, and hence can be extended to other complex models.
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    Traveling wave solutions of generalized seventh- order time-fractional KdV models through He-Laplace algorithm
    (Elsevier, 2023) Qayyum, Mubashir; Ahmad, Efaza; Saeed, Syed Tauseef; Akgul, Ali; Riaz, Muhammad Bilal
    Non-linear evolution equations play a prominent role in describing a wide range of phe-nomena in optical fibers, fluid dynamics, electromagnetic radiation, plasma and solid state physics. An important category of non-linear evolution models that characterizes shallow wave phenomena are the Korteweg-de Vries (KdV) models. In this regard, time-fractional Korteweg-de Vries models of seventh order are the main focus of this research. A general KdV seventh-order equation is con-sidered with different coefficients to form Lax, Kaup-Kuperschimdt and Sawada-Kotera-Ito KdV models. An efficient semi-analytical algorithm named as He-Laplace (HLM) is applied for the solu-tion of these models. In this algorithm, Laplace transform is hybrid with homotopy perturbation method (HPM). This study provides important results as non-linear evolution seventh-order models in fractional sense have not been captured through HLM in current literature. Absolute errors are computed and compared with already existing results to confirm the superiority of proposed algo-rithm over other existing techniques. Numerical and graphical investigations are conducted to eval-uate the approximate series form solutions. The dynamic behavior of fractional parameter is observed by calculating residual errors and plotting two dimensional diagrams throughout the fractional-domain. Analysis confirms that the proposed methodology provides an effective and con-venient way for solving fractional KdV models. (c) 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).