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    Öğe
    Iterative solutions for nonlinear equations via fractional derivatives: adaptations and advances
    (Taylor & Francis Ltd, 2024) Ali, Nasir; Waseem, Muhammad; Safdar, Maimoona; Akgul, Ali; Tolasa, Fikadu Tesgera
    In recent years, the utilization of fractional calculus has witnessed a notable surge across various scientific and engineering domains. This manuscript delves into the exploration of adapted iterative techniques tailored for solving nonlinear equations, capitalizing on the diverse range of derivatives available for addressing different problem contexts. We scrutinize previously developed iterative methods, enhancing their efficacy by introducing an auxiliary parameter to the root search process for nonlinear equations (NLE), alongside a fixed order of fractional derivatives. The selection of the auxiliary parameter is confined to the interval (0,1] for convenience. A thorough convergence analysis is conducted, employing a fractional power series expansion of f(x) in terms of fractional derivatives. Subsequently, a series of NLEs is solved to showcase and contrast the efficiency of our proposed methods with established iterative techniques. This refined abstract aims to succinctly elucidate the objectives and contributions of our study, providing readers with a clearer understanding of the manuscript's scope and significance.
  • [ X ]
    Öğe
    On study of flow features of hybrid nanofluid subjected to oscillatory disk
    (World Scientific Publ Co Pte Ltd, 2024) Safdar, Maimoona; Mushtaq, Tahir; Ali, Nasir; Akguel, Ali
    In recent years, an entirely new class of nanofluids has been developed, namely hybrid nanofluids. Their efficiency when it comes to heat transfer has been demonstrated to be much higher than the traditional nanofluids. In this study, the flow of hybrid nanofluid is analyzed subjected to the flow geometry of oscillatory disk that also rotates with the constant angular speed. Mainly, we investigated hybrid nanofluid flow subjected to an oscillatory disk that rotates at a constant angular speed as an incompressible, laminar and time-dependent electrically conducting flow. The implication of similarity functions normalizes the flow phenomenon. Furthermore, we solved the governing system by implementing the finite differences, and then the iterative procedure is carried out with the help of Successive Over-Relaxation (SOR) technique. In the later part of the paper, graphical representation is given to discuss dimensionless factors in both scenarios of nanofluid and hybrid nanofluid.