Browsing by Author "Rehman, A.U."

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Dynamical and Sensitivity Analysis for Fractional Kundu–eckhaus System To Produce Solitary Wave Solutions Via New Mapping Approach
(Taylor and Francis Ltd., 2024) Rehman, A.U.; Riaz, M.B.; Tunç, O.
The fractional Kundu–Eckhaus (FKE) equation, a nonlinear mathematical model, holds significance in assessing optical fibre communication systems. It takes into account various factors, including dispersion, noise and nonlinearity, which can impact the quality of signal and rates of data transmission in the systems of optical fibre. Utilizing the FKE model can contribute to optimizing the features of optical fibre network. In this academic investigation, an innovative mapping approach is applied to the FKE model to unveil novel soliton solutions. This is achieved through the utilization of beta derivative by employing the new mapping method and computer algebraic system such as Maple. The derived results are expressed in terms of hyperbolic and trigonometric functions. Our study elucidates a variety of soliton patterns such as periodic, dark, kink, bright, singular, dark–bright soliton solutions. To facilitate comprehension, certain solutions are visually depicted through two-dimensional, three-dimensional, and phase plots depicting bifurcation characteristics utilizing Maple software. Furthermore, the sensitivity of the model is explored across diverse initial conditions. Our study establishes a connection between computer science and soliton physics, emphasizing the pivotal role of soliton phenomena in advancing simulations and computational modelling. © 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the University of Bahrain.
Thermal and Flow Properties of Jeffrey Fluid Through Prabhakar Fractional Approach: Investigating Heat and Mass Transfer With Emphasis on Special Functions
(Springer, 2024) Riaz, M.B.; Rehman, A.U.; Chan, C.K.; Zafar, A.A.; Tunç, O.
The core purpose of this work is the investigation, formulation and develop a mathematical model by dint of a new fractional modeling approach namely Prabhakar fractional operator to study the dynamics of Jeffrey fluid flow and heat transfer phenomena. Exact analysis of natural convective flow of the Jeffrey fluid to derive analytical solutions with the non-integer order derivative Prabhakar fractional operator with non-singular type kernel alongwith application of generalized laws namely Fick’s and Fourier’s are reported here. This fractional operator has multi parameter generalized Mittag-Leffler kernel. The fluid flow is elaborated near an infinitely vertical plate with characteristics velocity u0. The modeling of the considered problem is done in terms of the partial differential equations together with generalized boundary conditions. Introduced the appropriate set of variables to transform the governing equations into dimensionless form. Laplace transform is operated on the fractional system of equations and results are presented in series form and also presented the solution in the form of special functions. The pertinent parameter’s influence such as α, Pr, β, Gm, Sc, γ, Gr on the fluid flow is brought under consideration to reveal the interesting results. In comparison, we noticed the Prabhakar-like non integer approach shows better results than the existing operators in the literature, and graphs are drawn to show the results. Also, obtained the results in a limiting sense such as second grade fluid, Newtonian fluid in fractionalized form as well as Jeffrey and viscous fluid models for classical form from Prabhakar-like non integer Jeffrey fluid model. © The Author(s), under exclusive licence to Springer Nature India Private Limited 2024.