WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

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Publisher: search.filters.publisher.SpringerSubject: search.filters.subject.Existence

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Now showing 1 - 4 of 4
  • Article
    Citation - WoS: 56
    Citation - Scopus: 67
    On Hilfer Generalized Proportional Fractional Derivative
    (Springer, 2020) Kumam, Poom; Jarad, Fahd; Borisut, Piyachat; Jirakitpuwapat, Wachirapong; Ahmed, Idris
    Motivated by the Hilfer and the Hilfer-Katugampola fractional derivative, we introduce in this paper a new Hilfer generalized proportional fractional derivative, which unifies the Riemann-Liouville and Caputo generalized proportional fractional derivative. Some important properties of the proposed derivative are presented. Based on the proposed derivative, we consider a nonlinear fractional differential equation with nonlocal initial condition and show that this equation is equivalent to the Volterra integral equation. In addition, the existence and uniqueness of solutions are proven using fixed point theorems. Furthermore, we offer two examples to clarify the results.
  • Article
    Citation - WoS: 14
    Citation - Scopus: 18
    On Existence-Uniqueness Results for Proportional Fractional Differential Equations and Incomplete Gamma Functions
    (Springer, 2020) Jarad, Fahd; Laadjal, Zaid; Abdeljawad, Thabet
    In this article, we employ the lower regularized incomplete gamma functions to demonstrate the existence and uniqueness of solutions for fractional differential equations involving nonlocal fractional derivatives (GPF derivatives) generated by proportional derivatives of the form D-rho=(1-rho)+rho D, rho is an element of[0,1], (1) where D is the ordinary differential operator.
  • Article
    Citation - WoS: 19
    Citation - Scopus: 24
    A Coupled System of Generalized Sturm-Liouville Problems and Langevin Fractional Differential Equations in the Framework of Nonlocal and Nonsingular Derivatives
    (Springer, 2020) Alzabut, J.; Jonnalagadda, J. M.; Adjabi, Y.; Matar, M. M.; Baleanu, D.
    In this paper, we study a coupled system of generalized Sturm-Liouville problems and Langevin fractional differential equations described by Atangana-Baleanu-Caputo (ABC for short) derivatives whose formulations are based on the notable Mittag-Leffler kernel. Prior to the main results, the equivalence of the coupled system to a nonlinear system of integral equations is proved. Once that has been done, we show in detail the existence-uniqueness and Ulam stability by the aid of fixed point theorems. Further, the continuous dependence of the solutions is extensively discussed. Some examples are given to illustrate the obtained results.
  • Article
    Citation - WoS: 9
    Citation - Scopus: 8
    On a System of Fractional Coupled Hybrid Hadamard Differential Equations With Terminal Conditions
    (Springer, 2020) Karthikeyan, Panjaiyan; Baleanu, Dumitru; Buvaneswari, Karthikeyan
    In this manuscript, we study the existence of solutions for a coupled system of nonlinear hybrid differential equations of fractional order involving Hadamard derivative with nonlocal boundary conditions. By using suitable fixed point theorems we establish sufficient conditions for the existence result. An example is provided to illustrate our main result.