Scopus İndeksli Yayınlar Koleksiyonu

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

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Author: search.filters.author.Baleanu, DumitruSubject: search.filters.subject.Fixed Point Theorems

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Now showing 1 - 6 of 6
  • Article
    Citation - WoS: 46
    Citation - Scopus: 52
    Analysis of the Fractional Tumour-Immune Model With Mittag-Leffler Kernel
    (Elsevier, 2020) Ullah, Aman; Akgul, Ali; Baleanu, Dumitru; Ahmad, Shabir
    Recently, Atangana-Baleanu fractional derivative has got much attention of the researchers due to its nonlocality and non-singularity. This operator contains an accurate kernel that describes the better dynamics of systems with a memory effect. In this paper, we investigate the fractional-order tumour-immune-vitamin model (TIVM) under Mittag-Leffler derivative. The existence of at least one solution and a unique solution has discussed through fixed point results. We established the Hyres-Ulam stability of the proposed model under the Mittag-Leffler derivative. The fractional Adams-Bashforth method has used to achieve numerical results. Finally, we simulate the obtained numerical results for different fractional orders to show the effect of vitamin intervention on decreased tumour cell growth and cancer risk. At the end of the paper, the conclusion has provided.
  • Article
    Citation - WoS: 66
    Citation - Scopus: 76
    Existence of Solutions of Non-Autonomous Fractional Differential Equations With Integral Impulse Condition
    (Springer, 2020) Chauhan, Harsh Vardhan Singh; Ravichandran, Chokkalingam; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Kumar, Ashish
    In this paper, we investigate the existence of solution of non-autonomous fractional differential equations with integral impulse condition by the measure of non-compactness (MNC), fixed point theorems, andk-set contraction. The obtained results are verified via a supporting example.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 11
    On the Solutions of a Fractional Boundary Value Problem
    (Tubitak Scientific & Technological Research Council Turkey, 2018) Ugurlu, Ekin; Baleanu, Dumitru; Tas, Kenan
    This paper is devoted to showing the existence and uniqueness of solution of a regular second-order nonlinear fractional differential equation subject to the ordinary boundary conditions. The Banach fixed point theorem is used to prove the results.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 1
    A Fixed Point Theorem on Multiplicative Metric Space With Integral-Type Inequality
    (Journal Mathematics & Computer Science-jmcs, 2018) Khan, Hasib; Baleanu, Dumitru; Jafari, Hossein; Khan, Tahir Saeed; Alqurashi, Maysaa; Khan, Aziz
    In this paper, we prove fixed point theorems (FPTs) on multiplicative metric space (MMS) (X, triangle) by the help of integral-type contractions of self-quadruple mappings (SQMs), i.e., for p(1), p(2), p(3), p(4) : X -> R. For this, we assume that the SQMs are weakly compatible mappings and the pairs (p(1), p(3)) and (p(2), p(4)) satisfy the property (CLRp3p4). Further, two corollaries are produced from our main theorem as special cases. The novelty of these results is that for the unique common fixed point (CFP) of the SQMs p(1), p(2), p(3), p(4), we do not need to the assumption of completeness of the MMS (X, triangle). These results generalize the work of Abdou, [A. A. N. Abdou, J. Nonlinear Sci. Appl., 9 (2016), 2244-2257], and many others in the available literature.
  • Article
    On the solutions of a fractional boundary value problem
    (Scientific Technical Research Council Turkey-Tubitak, 2018) Uğurlu, Ekin; Baleanu, Dumitru; Taş, Kenan
    This paper is devoted to showing the existence and uniqueness of solution of a regular second-order nonlinear fractional differential equation subject to the ordinary boundary conditions. The Banach fixed point theorem is used to prove the results.
  • Article
    Citation - WoS: 45
    Citation - Scopus: 53
    Existence Criterion for the Solutions of Fractional Order P-Laplacian Boundary Value Problems
    (Springer, 2015) Baleanu, Dumitru; Khan, Hasib; Khan, Rahmat Ali; Khan, Aziz; Jafari, Hossein
    The existence criterion has been extensively studied for different classes in fractional differential equations (FDEs) through different mathematical methods. The class of fractional order boundary value problems (FOBVPs) with p-Laplacian operator is one of the most popular class of the FDEs which have been recently considered by many scientists as regards the existence and uniqueness. In this scientific work our focus is on the existence and uniqueness of the FOBVP with p-Laplacian operator of the form: D-gamma(phi(p)(D-theta z(t))) + a(t)f(z(t)) = 0, 3 < theta, gamma <= 4, t is an element of [0, 1], z(0) = z'''(0), eta D(alpha)z(t)vertical bar(t=1) = z'(0), xi z ''(1) - z ''(0) = 0, 0 < alpha < 1, phi(p)(D-theta z(t))vertical bar(t=0) = 0 = (phi(p)(D-theta z(t)))'vertical bar(t=0), (phi(p)(D-theta z(t)))''vertical bar(t=1) = 1/2(phi(p)(D-theta z(t)))''vertical bar(t=0), (phi(p)(D-theta z(t)))'''vertical bar(t=0) = 0, where 0 < xi, eta < 1 and D-theta, D-gamma, D-alpha are Caputo's fractional derivatives of orders theta, gamma, alpha, respectively. For this purpose, we apply Schauder's fixed point theorem and the results are checked by illustrative examples.