Scopus İndeksli Yayınlar Koleksiyonu

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

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Scopus Q: search.filters.scopusQuartile.Q4Subject: search.filters.subject.Fixed Point Theory

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  • Article
    Citation - WoS: 7
    Citation - Scopus: 7
    On the Existence and Uniqueness of Solution of a Nonlinear Fractional Differential Equations
    (Eudoxus Press, Llc, 2013) Darzi, R.; Baleanu, Dumitru; Mohammadzadeh, B.; Neamaty, A.; Baleanu, D.; Matematik
    In this paper, we investigate the existence and uniqueness of solution for fractional boundary value problem for nonlinear fractional differential equation D-0+(alpha) u(t) = f(t,u(t)), 0 < t < 1, 2 < alpha <= 3, with the integral boundary conditions {u(0) - gamma(1) u(1) = lambda(1) integral(1)(0) g(1) (s, u(s))ds, u'(0) - gamma(2)u'(1) = lambda(2) integral(1)(0) g(2) (s, u(s))ds, u ''(0) - gamma(2)u ''(1) = 0, where D-0+(alpha) denotes Caputo derivative of order alpha. by using the fixed point theory. We apply the contraction mapping principle and Krasnoselskii's fixed point theorem to obtain some new existence and uniqueness results. Two examples are given to illustrate the main results.
  • Book Part
    Introduction
    (Springer Nature, 2022) Karapınar, Erdal; Agarwal, Ravi P.
    Fixed point theory can be described as a framework for researching and investigating the existence of the solution of the equation f(p) = p for a certain self-mapping f that is defined on a non-empty set X. As is expected, here, p is called the fixed point of the mapping f. On the other side, we may re-consider the fixed point equation f(p) = p as T(p) = f(p) - p= 0 and, accordingly, finding the zeros of the mapping T and finding the fixed point of f becomes an equivalent statement. This equivalence, not only enriches the fixed point theory but also, opens the doors to a wide range of potential applications in the setting of almost all quantitative sciences. For example, let us consider one of the classical open problems of number theory, finding perfect numbers: Let p be a self-mapping on a natural number such that p(n) is the sum of all divisors of n for n&gt; 1. Thus, any fixed points of the function p give a perfect number. In particular, 6 is the smallest perfect numbers, and 2 74207280× (2 74207281- 1 ), with 44, 677, 235 digits, is the biggest known perfect number. © 2022 Elsevier B.V., All rights reserved.