Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 12Citation - Scopus: 17Thermal and Concentration Diffusion Impacts on Mhd Maxwell Fluid: a Generalized Fourier's and Fick's Perspective(Elsevier, 2022) Rehman, Aziz Ur; Riaz, Muhammad Bilal; Atangana, Abdon; Jarad, Fahd; Awrejcewicz, JanIn this article, a new approach to study the fractionalized Maxwell fluid is described by the Prabhakar fractional derivative near an exponentially accelerated vertical plate together with exponentially variable velocity, energy and mass diffusion through a porous media is critically examined. The phenomena has been described in forms of partial differential equations along with heat and mass transportation effect taken into account. The Prabhakar fractional operator which was recently introduced is used in this work together with generalized Fick's and Fourier's law. The fractionalized model is transfromed into non-dimensional form by using some suitable dimensionless quantities. The non-dimensional developed fractional model for momentum, thermal and diffusion equations based on Prabhakar fractional operator has been solved analytically via Laplace transformation method and calculated solutions expressed in terms of Mittag-Leffler special functions. Graphical demonstration are made to characterized the physical behavior of different parameters and significance of such system parameters over the momentum, concentration and energy profiles. Moreover, for results validation, comparative study among limiting models derived from fractionalized Prabhakar Maxwell fluid such as fractional and classical fluid models for Maxwell and Newtonian are performed. Further, it is observed from the graphs the valocity curves for classical fluid models relatively higher as compared to fractional fluid models, and fractional approach is more realistic and convenient as compared to classical approach.Article Citation - WoS: 19Citation - Scopus: 20New Optical Solitons of Fractional Nonlinear Schrodinger Equation With the Oscillating Nonlinear Coefficient: a Comparative Study(Elsevier, 2022) Riaz, Muhammad Bilal; Atangana, Abdon; Jahngeer, Adil; Jarad, Fahd; Awrejcewicz, JanIn this current exploration, some new optical soliton structures of fractional nonlinear Schrodinger equation with the oscillating nonlinear coefficient are constructed with three different definitions of fractional operators beta, Riemann-Liouville, and M-Truncated derivatives. These structures are computed with the help of the new auxiliary equation method. This method gives the new analytical solutions of the considered model. The analysis is done by considering the different definitions of the derivatives like Beta, Riemann-Liouville (RL), and M-Truncated derivatives. The considered equation is converted to an ordinary differential equation (ODE) by the use of this complex transformation. The graphical explanation of some obtained results is also elaborated in detail. This work is new and does not exist in literature.Article Citation - WoS: 25Citation - Scopus: 29Investigation of Wave Solutions and Conservation Laws of Generalized Calogero-Bogoyavlenskii Equation by Group Theoretic Method(Elsevier, 2022) Jarad, Fahd; Jhangeer, Adil; Awrejcewicz, Jan; Riaz, Muhammad Bilal; Junaid-U-Rehman, M.This work is focused to analyze the generalized Calogero-Bogoyavlenskii-Schiff equation (GCBSE) by the Lie symmetry method. GCBS equation has been utilized to explain the wave profiles in soliton theory. GCBSE was constructed by Bogoyavlenskii and Schiff in different ways (explained in the introduction section). With the aid of Lie symmetry analysis, we have computed the symmetry generators of the GCBSE and commutation relation. We observed from the commutator table, translational symmetries make an Abelian algebra. Then by using the theory of Lie, we have discovered the similarity variables, which are used to convert the supposed nonlinear partial differential equation (NLPDE) into a nonlinear ordinary differential equation (NLODE). Using the new auxiliary method (NAM), we have to discover some new wave profiles of GCBSE in the type of few trigonometric functions. These exits some parameters which we give to some suitable values to attain the different diagrams of some obtained solutions. Further, the GCBSE is presented by non-linear self-adjointness, and conserved vectors are discovered corresponding to each generator.Article Citation - WoS: 14Citation - Scopus: 33Exact Solutions for Thermomagetized Unsteady Non-Singularized Jeffrey Fluid: Effects of Ramped Velocity, Concentration With Newtonian Heating(Elsevier, 2021) Riaz, Muhammad Bilal; Awrejcewicz, Jan; Baleanu, Dumitru; Aziz-Ur-RehmanThe classical calculus due to the fact that it assumed as the instant rate of change of the output, when the input level changes. Therefore it is not able to include the previous state of the system called memory effect. But in the Fractional Calculus (FC), the rate of change is affected by all points of the considered interval, so it is able to incorporate the previous history/memory effects of any system. Due to the importance of this effect we used the modern concept of the Caputo-Fabrizio fractional derivative on the considered Jeffrey fluid model. In this paper the effect of Newtonian heating, concentration and velocity on unsteady MHD free convective flow of Jeffrey fluid over long vertical an infinite ramped wall nested in porous material are discussed. Exact analytical solutions are derived via Laplace transformation technique for principal equations of energy, concentration and ramped velocity. The prime features of various coherent parameters are deliberated and illuminated with the aid of plotted graphs. A comparative study to show the significance of fractional order model with an integer order model is accomplished. The fractional order model is found to be the best choice for explaining the memory effect of the considered problem. It is identified that temperature distribution, concentration and ramped velocity profiles for fractional model are converges to an ordinary model when fractional parameter tends to integer order, which shows that fractional model is more appropriate to explicate experimental results.Article Exact solutions for thermomagetized unsteady non-singularized jeffrey fluid: Effects of ramped velocity, concentration with newtonian heating(Elsevier, 2021) Aziz-Ur, Rehman; Riaz, Muhammad Bilal; Awrejcewicz, Jan; Baleanu, Dumitru; Aziz-ur-rehman,The classical calculus due to the fact that it assumed as the instant rate of change of the output, when the input level changes. Therefore it is not able to include the previous state of the system called memory effect. But in the Fractional Calculus (FC), the rate of change is affected by all points of the considered interval, so it is able to incorporate the previous history/memory effects of any system. Due to the importance of this effect we used the modern concept of the Caputo-Fabrizio fractional derivative on the considered Jeffrey fluid model. In this paper the effect of Newtonian heating, concentration and velocity on unsteady MHD free convective flow of Jeffrey fluid over long vertical an infinite ramped wall nested in porous material are discussed. Exact analytical solutions are derived via Laplace transformation technique for principal equations of energy, concentration and ramped velocity. The prime features of various coherent parameters are deliberated and illuminated with the aid of plotted graphs. A comparative study to show the significance of fractional order model with an integer order model is accomplished. The fractional order model is found to be the best choice for explaining the memory effect of the considered problem. It is identified that temperature distribution, concentration and ramped velocity profiles for fractional model are converges to an ordinary model when fractional parameter tends to integer order, which shows that fractional model is more appropriate to explicate experimental results. © 2021