Scopus İndeksli Yayınlar Koleksiyonu

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

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  • Article
    Citation - WoS: 14
    Citation - Scopus: 14
    Boundary Value Problem of Weighted Fractional Derivative of a Function With a Respect To Another Function of Variable Order
    (Springer, 2023) Jarad, Fahd; Alqudah, Manar A.; Abdeljawad, Thabet; Benia, Kheireddine; Souid, Mohammed Said
    This study aims to resolve weighted fractional operators of variable order in specific spaces. We establish an investigation on a boundary value problem of weighted fractional derivative of one function with respect to another variable order function. It is essential to keep in mind that the symmetry of a transformation for differential equations is connected to local solvability, which is synonymous with the existence of solutions. As a consequence, existence requirements for weighted fractional derivative of a function with respect to another function of constant order are necessary. Moreover, the stability with in Ulam-Hyers-Rassias sense is reviewed. The outcomes are derived using the Kuratowski measure of non-compactness. A model illustrates the trustworthiness of the observed results.
  • Article
    Citation - WoS: 33
    Citation - Scopus: 39
    An Efficient Technique for Fractional Coupled System Arisen in Magnetothermoelasticity With Rotation Using Mittag-Leffler Kernel
    (Asme, 2021) Prakasha, D. G.; Baleanu, Dumitru; Veeresha, P.
    In this paper, we find the solution for fractional coupled system arisen in magnetothermoelasticity with rotation using q-homotopy analysis transform method ( q-HATM). The proposed technique is graceful amalgamations of Laplace transform technique with q-homotopy analysis scheme, and fractional derivative defined with Mittag-Leffler kernel. The fixed point hypothesis is considered to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional order model. To illustrate the efficiency of the future technique, we analyzed the projected model in terms of fractional order. Moreover, the physical behavior of q-HATM solutions has been captured in terms of plots for different arbitrary order. The attained consequences confirm that the considered algorithm is highly methodical, accurate, very effective, and easy to implement while examining the nature of fractional nonlinear differential equations arisen in the connected areas of science and engineering.
  • Article
    Citation - WoS: 102
    Citation - Scopus: 120
    A Fractional Model for the Dynamics of Tuberculosis Infection Using Caputo-Fabrizio Derivative
    (Amer inst Mathematical Sciences-aims, 2020) Khan, Muhammad Altaf; Farooq, Muhammad; Hammouch, Zakia; Baleanu, Dumitru; Ullah, Saif
    In the present paper, we study the dynamics of tuberculosis model using fractional order derivative in Caputo-Fabrizio sense. The number of confirmed notified cases reported by national TB program Khyber Pakhtunkhwa, Pakistan, from the year 2002 to 2017 are used for our analysis and estimation of the model biological parameters. The threshold quantity R-0 and equilibria of the model are determined. We prove the existence of the solution via fixed-point theory and further examine the uniqueness of the model variables. An iterative solution of the model is computed using fractional Adams-Bashforth technique. Finally, the numerical results are presented by using the estimated values of model parameters to justify the significance of the arbitrary fractional order derivative. The graphical results show that the fractional model of TB in Caputo-Fabrizio sense gives useful information about the complexity of the model and one can get reliable information about the model at any integer or non-integer case.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 3
    Analysis of Mixed-Order Caputo Fractional System With Nonlocal Integral Boundary Condition
    (Tubitak Scientific & Technological Research Council Turkey, 2018) Khodabakhshi, Neda; Baleanu, Dumitru; Akman Yildiz, Tugba; Yıldız, Tuğba Akman
    This paper deals with a mixed-order Caputo fractional system with nonlocal integral boundary conditions. This study can be considered as an extension of previous studies, since the orders of the equations lie on different intervals. We discuss the existence and uniqueness of the solution using fixed point methods. We enrich the study with an example.