Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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  • Article
    Citation - Scopus: 7
    On the Discrete Laplace Transform
    (Cankaya University, 2019) Ameen, R.; Jarad, Fahd; Köse, H.; Jarad, F.; Matematik
    The objective of this paper is to introduce the discrete Laplace transform. Basic theorems related to this transformation are mentioned and the discrete Laplace transform of basic functions are given. © 2019, Cankaya University. All rights reserved.
  • Article
    Citation - Scopus: 5
    Chaos in New 2-D Discrete Mapping and Its Application in Optimization
    (InforMath Publishing Group, 2020) Bououden, R.; Jarad, Fahd; Abdelouahab, M.S.; Jarad, F.; Matematik
    In this paper, we propose a new map which is a combination of the Hénon and Lozi maps. We analyze the proposed map numerically and with the aid of bifurcation plots. On the other hand, and as an example of application of this new map, we are going to use it in the chaotic optimisation algorithm. To prove the efficiency of this map, we use numerical results thorought the paper. © 2020 InforMath Publishing Group
  • Editorial
    A Special Issue in Honor of the 55th Birthday of Dumitru Baleanu
    (Cankaya University, 2019) Jarad, F.; Jarad, Fahd; Matematik
  • Article
    Citation - Scopus: 9
    A Dynamical and Sensitivity Analysis of the Caputo Fractional-Order Ebola Virus Model: Implications for Control Measures
    (Thammasat University, 2023) Ahmed, I.; Jarad, Fahd; Yusuf, A.; Tariboon, J.; Muhammad, M.; Jarad, F.; Mikailu, B.B.; Matematik
    The recurrence of outbreaks in cases of Ebola virus among African countries remains one of the greatest issues of concern. Practices such as hunting or consumption of contam-inated bush meat, unsafe funeral practices, and environmental contamination have all been implicated as possible contributors. This paper investigates the transmission dynamics of the Ebola virus model in the setting of a Caputo fractional-order derivative that accounts for both direct and indirect transmissions of the virus. By employing the concept of fixed theorems, we derived the existence and uniqueness results of the model. Moreover, we analyzed the forward normalized sensitivity indices to identify the critical parameters for controlling the infection and found that reducing the contact rate between infected individuals and susceptible vectors is vital to limiting the virus’s spread. Comparing the proposed fractional-order model with those of the previously developed integer-order model numerically, we found that the proposed model provides more reliable information on the model’s dynamics. Thus, we conclude that the Caputo fractional-order operator is a precise tool for describing the proposed model behavior and can help understand the complexities of Ebola virus disease outbreaks. © 2023, Thammasat University. All rights reserved.
  • Article
    Citation - Scopus: 2
    Existence of Solutions of Multi-Order Fractional Differential Equations
    (Elsevier B.V., 2025) Bouchelaghem, F.; Boulares, H.; Ardjouni, A.; Jarad, F.; Abdeljawad, T.; Abdalla, B.; Shah, K.
    Recently, the field of fractional calculus has garnered significant attention due to its wide range of applications across various disciplines in science and engineering. Numerous results have been derived using tools from numerical functional analysis and fixed point theory to address a variety of problems in this area. This study employs the Banach Fixed Point Theorem (BFPT) to establish the existence and uniqueness of solutions for Riemann–Liouville fractional differential equations (RLFDEs) involving multiple orders. Sufficient conditions for the existence of solutions to the problem under consideration have been provided. Furthermore, an illustrative example is presented to validate the theoretical findings. © 2025
  • Article
    Citation - Scopus: 7
    Numerical Evaluation for the Peristaltic Flow in the Proximity of Double-Diffusive Convection of Non-Newtonian Nanofluid Under the Mhd
    (Elsevier B.V., 2024) Riaz, M.B.; Hussain, A.; Saddiqa, A.; Jarad, F.
    This article mainly studies the 2-D propagation of a non-compressible Eyring-Powell nanofluid flow through a stretched wedge under the Magneto-hydrodynamic effect. Equations for temperature, concentration, double-diffusive convection and momentum are taken into consideration. Since solving the dimensionless equations associated with our study is an uphill task, we utilize the MATLAB bvp4c solver to illustrate the graphical performance of different parameters. This manuscript may be significant in the projects in the field of industry and medicine. The manuscript's noteworthy features include the magnetic field, heat source-sink parameter, double diffusivity, and solar radiation process. The main finding is that the local fluid parameter k1 and magnetic field parameter M decelerate the velocity of nanofluid. Because different nanoparticles have different effects on fluids, the fluid's temperature exhibits multiple behaviors, therefore by escalating the Prandtl number initially, it increases and then decelerates due to the presence of nanoparticles. The concentration of fluid declines as the Schmidt number rises. The double diffusivity of Eyring-Powell nanofluid improves with magnification in the fluid's Schmidt number Sc and Prandtl number Pr. © 2024 The Author(s)
  • Book Part
    Strange Chaotic Attractors and Existence Results Via Nonlinear Fractional Order Systems and Fixed Points
    (Springer, 2024) Panda, S.K.; Vijayakumar, V.; Gopinadh, B.S.; Jarad, F.
    An analog of Meir-Keeler’s fixed point result in suprametric space is proved in this paper, and application to strange attractors in the context of the Atangana-Baleanu derivative is discussed. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.
  • Other
    Citation - Scopus: 14
    Multicriteria Decision-Making Approach for Pythagorean Fuzzy Hypersoft Sets' Interaction Aggregation Operators
    (Hindawi Limited, 2021) Zulqarnain, R.M.; Siddique, I.; Ali, R.; Jarad, F.; Iampan, A.
    In this paper, we examine the multicriteria decision-making (MCDM) difficulties for Pythagorean fuzzy hypersoft sets (PFHSSs). The PFHSSs are a suitable extension of the Pythagorean fuzzy soft sets (PFSSs) which deliberates the parametrization of multi-subattributes of considered parameters. It is a most substantial notion for describing fuzzy information in the decision-making (DM) procedure to accommodate more vagueness comparative to existing PFSSs and intuitionistic fuzzy hypersoft sets (IFHSSs). The core objective of this study is to plan some innovative operational laws considering the interaction for Pythagorean fuzzy hypersoft numbers (PFHSNs). Also, based on settled interaction operational laws, two aggregation operators (AOs) i.e., Pythagorean fuzzy hypersoft interaction weighted average (PFHSIWA) and Pythagorean fuzzy hypersoft interaction weighted geometric (PFHSIWG) operators for PFHSSs operators have been presented with their fundamental properties. Furthermore, an MCDM technique has been established using planned interaction AOs. To ensure the strength and practicality of the developed MCDM method, a mathematical illustration has been presented. The usefulness, influence, and versatility of the developed method have been demonstrated via comparative analysis with the help of some conventional studies. © 2021 Rana Muhammad Zulqarnain et al.
  • Article
    Citation - Scopus: 4
    Numerical Construction of Lyapunov Functions Using Homotopy Continuation Method
    (DergiPark, 2022) Bala, S.I.; Ahmed, I.; Ibrahim, M.J.; Jarad, F.; Ibrahim, A.
    Lyapunov functions are commonly involved in the analysis of the stability of linear and nonlinear dynamical systems. Despite the fact that there is no generic procedure for creating these functions, many authors use polynomials in p-forms as candidates for constructing Lyapunov functions, while others restrict the construction to quadratic forms. We proposed a method for constructing polynomial Lyapunov functions that are not necessary in a form by focusing on the positive and negative definiteness of the Lyapunov candidate and the Hessian of its derivative, as well as employing the sum of square decomposition. The idea of Newton polytopes was used to transform the problem into a system of algebraic equations that were solved using the polynomial homotopy continuation method. Our method can produce several possibilities of Lyapunov functions for a given candidate. The sample test conducted demonstrates that the method developed is promising. © 2022, DergiPark. All rights reserved.
  • Article
    Citation - Scopus: 19
    Mittag-Leffler Form Solutions of Natural Convection Flow of Second Grade Fluid With Exponentially Variable Temperature and Mass Diffusion Using Prabhakar Fractional Derivative
    (Elsevier Ltd, 2022) Awrejcewicz, J.; Riaz, M.B.; Jarad, F.; Rehman, A.U.
    In this article, heat source impact on unsteady magnetohydrodynamic (MHD) flows of Prabhakar-like non integer second grade fluid near an exponentially accelerated vertical plate with exponentially variable velocity, temperature and mass diffusion through a porous medium. For the sake of generalized memory effects, a new mathematical fractional model is formulated based on 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 α, Pr, β, Sc, Gr, γ, Gm are studied and demonstrated graphically by Mathcad software. Furthermore, to validate our current results, some limiting models such as classical second grade model, classical Newtonian model and fractional Newtonian model are recovered from Prabhakar fractional second grade fluid. Moreover, compare the results between second grade and Newtonian fluids for both fractional and classical which shows that the movement of the viscous fluid is faster than second grade fluid. Additionally, it is visualized that for both classical second grade and viscous fluid have relatively higher velocity as compared to fractional second grade and viscous fluid. © 2022 The Authors.