Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article The Hausdorff-Pompeiu Distance in Gn-Menger Fractal Spaces(Mdpi, 2022) Saadati, Reza; Li, Chenkuan; Jarad, Fahd; O'Regan, Donal; O’Regan, DonalThis paper introduces a complete Gn-Menger space and defines the Hausdorff-Pompeiu distance in the space. Furthermore, we show a novel fixed-point theorem for Gn-Menger-theta-contractions in fractal spaces.Article Citation - WoS: 27Citation - Scopus: 28On Dynamic Systems in the Frame of Singular Function Dependent Kernel Fractional Derivatives(Mdpi, 2019) Jarad, Fahd; Sene, Ndolane; Abdeljawad, Thabet; Madjidi, FadilaIn this article, we discuss the existence and uniqueness theorem for differential equations in the frame of Caputo fractional derivatives with a singular function dependent kernel. We discuss the Mittag-Leffler bounds of these solutions. Using successive approximation, we find a formula for the solution of a special case. Then, using a modified Laplace transform and the Lyapunov direct method, we prove the Mittag-Leffler stability of the considered system.Article Citation - WoS: 7Citation - Scopus: 6New Solutions of Nonlinear Dispersive Equation in Higher-Dimensional Space With Three Types of Local Derivatives(Mdpi, 2022) Hashemi, Mir Sajjad; Jarad, Fahd; Akgul, AliThe aim of this paper is to use the Nucci's reduction method to obtain some novel exact solutions to the s-dimensional generalized nonlinear dispersive mK(m,n) equation. To the best of the authors' knowledge, this paper is the first work on the study of differential equations with local derivatives using the reduction technique. This higher-dimensional equation is considered with three types of local derivatives in the temporal sense. Different types of exact solutions in five cases are reported. Furthermore, with the help of the Maple package, the solutions found in this study are verified. Finally, several interesting 3D, 2D and density plots are demonstrated to visualize the nonlinear wave structures more efficiently.Article Citation - WoS: 27Citation - Scopus: 30Generalized Mittag-Leffler Kernel Form Solutions of Free Convection Heat and Mass Transfer Flow of Maxwell Fluid With Newtonian Heating: Prabhakar Fractional Derivative Approach(Mdpi, 2022) Jarad, Fahd; Riaz, Muhammad Bilal; Shah, Zaheer Hussain; Rehman, Aziz UrIn this article, the effects of Newtonian heating along with wall slip condition on temperature is critically examined on unsteady magnetohydrodynamic (MHD) flows of Prabhakar-like non integer Maxwell fluid near an infinitely vertical plate under constant concentration. For the sake of generalized memory effects, a new mathematical fractional model is formulated based on a newly introduced Prabhakar fractional operator with generalized Fourier's law and Fick's law. This fractional model has been solved analytically and exact solutions for dimensionless velocity, concentration, and energy equations are calculated in terms of Mittag-Leffler functions by employing the Laplace transformation method. Physical impacts of different parameters such as <mml:semantics>alpha</mml:semantics>, <mml:semantics>Pr</mml:semantics>, <mml:semantics>beta</mml:semantics>, <mml:semantics>Sc</mml:semantics>, <mml:semantics>Gr</mml:semantics>, <mml:semantics>gamma</mml:semantics>, and <mml:semantics>Gm</mml:semantics> are studied and demonstrated graphically by Mathcad software. Furthermore, to validate our current results, some limiting models such as classical Maxwell model, classical Newtonian model, and fractional Newtonian model are recovered from Prabhakar fractional Maxwell fluid. Moreover, we compare the results between Maxwell and Newtonian fluids for both fractional and classical cases with and without slip conditions, showing that the movement of the Maxwell fluid is faster than viscous fluid. Additionally, it is visualized that both classical Maxwell and viscous fluid have relatively higher velocity as compared to fractional Maxwell and viscous fluid.Article Citation - WoS: 20Citation - Scopus: 21Fractional Order Mathematical Model of Serial Killing With Different Choices of Control Strategy(Mdpi, 2022) Ahmad, Shabir; Arfan, Muhammad; Akgul, Ali; Jarad, Fahd; Rahman, Mati UrThe current manuscript describes the dynamics of a fractional mathematical model of serial killing under the Mittag-Leffler kernel. Using the fixed point theory approach, we present a qualitative analysis of the problem and establish a result that ensures the existence of at least one solution. Ulam's stability of the given model is presented by using nonlinear concepts. The iterative fractional-order Adams-Bashforth approach is being used to find the approximate solution. The suggested method is numerically simulated at various fractional orders. The simulation is carried out for various control strategies. Over time, all of the compartments demonstrate convergence and stability. Different fractional orders have produced an excellent comparison outcome, with low fractional orders achieving stability sooner.Article Citation - WoS: 1Citation - Scopus: 2Existence and Well-Posedness of Tripled Fixed Points With Application To a System of Differential Equations(Mdpi, 2022) Hammad, Hasanen A.; Nafea, Ahmed; Jarad, Fahd; Rashwan, Rashwan A.The purpose of this manuscript is to demonstrate the existence and uniqueness of triple fixed-point results for Geraghty-type contractions in ordinary metric spaces with binary relations. Moreover, the well-posedness of the tripled fixed point problem is investigated. Consequently, a-dominated mapping on such space is discussed. Ultimately, to promote our paper, some illustrative examples are derived, and the existence of the solution to a system of differential equations is obtained as an application.Article Citation - WoS: 5Citation - Scopus: 4Estimates for a Rough Fractional Integral Operator and Its Commutators on P-Adic Central Morrey Spaces(Mdpi, 2022) Jarad, Fahd; Sarfraz, NaqashIn the current paper, we obtain the boundedness of a rough p-adic fractional integral operator on p-adic central Morrey spaces. Moreover, we establish the lambda-central bounded mean oscillations estimate for commutators of a rough p-adic fractional integral operator on p-adic central Morrey spaces.Article Citation - WoS: 13Citation - Scopus: 15Impact of Newtonian Heating Via Fourier and Fick's Laws on Thermal Transport of Oldroyd-B Fluid by Using Generalized Mittag-Leffler Kernel(Mdpi, 2022) Rehman, Aziz Ur; Riaz, Muhammad Bilal; Jarad, Fahd; Sun, Xiang-E; Chen, Chunxia; Ur Rehman, AzizIn this manuscript, a new approach to study the fractionalized Oldroyd-B fluid flow based on the fundamental symmetry is described by critically examining the Prabhakar fractional derivative near an infinitely vertical plate, wall slip condition on temperature along with Newtonian heating effects and constant concentration. The phenomenon 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 fractional model is transfromed into a non-dimentional form by using some suitable quantities and the symmetry of fluid flow is analyzed. 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 demonstrations are made to characterize the physical behavior of different parameters and significance of such system parameters over the momentum, concentration and energy profiles. Moreover, to validate our current results, some limiting models such as fractional and classical fluid models for Maxwell and Newtonian are recovered, in the presence of with/without slip boundary wall conditions. Further, it is observed from the graphs the velocity curves for classical fluid models are relatively higher than fractional fluid models. A comparative analysis between fractional and classical models depicts that the Prabhakar fractional model explains the memory effects more adequately.Article Citation - WoS: 17Citation - Scopus: 17Double Diffusive Magneto-Free Flow of Oldroyd-B Fluid Over a Vertical Plate With Heat and Mass Flux(Mdpi, 2022) Rehman, Aziz Ur; Awrejcewicz, Jan; Jarad, Fahd; Riaz, Muhammad BilalThe purpose of this research is to analyze the general equations of double diffusive magneto-free convection in an Oldroyd-B fluid flow based on the fundamental symmetry that are presented in non-dimensional form and are applied to a moving heated vertical plate as the boundary layer flow up, with the existence of an external magnetic field that is either moving or fixed consistent with the plate. The thermal transport phenomenon in the presence of constant concentration, coupled with a first order chemical reaction under the exponential heating of the symmetry of fluid flow, is analyzed. The Laplace transform method is applied symmetrically to tackle the non-dimensional partial differential equations for velocity, mass and energy. The contribution of mass, thermal and mechanical components on the dynamics of fluid are presented and discussed independently. An interesting property regarding the behavior of the fluid velocity is found when the movement is observed in the magnetic intensity along with the plate. In that situation, the fluid velocity is not zero when it is far and away from the plate. Moreover, the heat transfer aspects, flow dynamics and their credence on the parameters are drawn out by graphical illustrations. Furthermore, some special cases for the movement of the plate are also studied.Article Citation - WoS: 1Citation - Scopus: 1Int N-Soft Substructures of Semigroups(Mdpi, 2023) Jawad, Muhammad; Naz, Munazza; Jarad, Fahd; Abdeljawad, Thabet; Shabir, Muhammad; Mushtaq, RimshaThe N-soft sets are newly defined structures with many applications in the real world. We aim for combining the semigroup theory and N-soft sets to provide a comprehensive account of the hybrid framework of N-soft Semigroups. In this paper, we define the gamma-inclusive set, int N-soft subsemigroups, int N-soft left [right] ideals of S, int N-soft product and int N-soft characteristic function, theta-Generalized int N-soft subsemigroups and theta-Generalized int N-soft left [right] ideals of S. We also discuss some examples and theorems based on the restricted (extended) union, restricted (extended) intersection, and gamma-inclusive set.