Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 12Citation - Scopus: 11Ulam-Hyers Stability for Tripled System of Weighted Fractional Operator With Time Delay(Springer, 2021) Jarad, Fahd; Abdeljawad, Thabet; Almalahi, Mohammed A.; Panchal, Satish K.This study is aimed to investigate the sufficient conditions of the existence of unique solutions and the Ulam-Hyers-Mittag-Leffler (UHML) stability for a tripled system of weighted generalized Caputo fractional derivatives investigated by Jarad et al. (Fractals 28:2040011 2020) in the frame of Chebyshev and Bielecki norms with time delay. The acquired results are obtained by using Banach fixed point theorems and the Picard operator (PO) method. Finally, a pertinent example of the results obtained is demonstrated.Article Citation - WoS: 5Citation - Scopus: 7Existence and Uniqueness of Positive Solutions for a New Class of Coupled System Via Fractional Derivatives(Springer, 2020) Sajjadmanesh, Mojtaba; Baleanu, Dumitru; Afshari, HojjatIn this paper we study the existence of unique positive solutions for the following coupled system: {Da0 + x(t) + f1(t, x(t), D. 0+ x(t)) + g1(t, y(t)) = 0, D beta 0+ y(t) + f2(t, y(t), D. 0+ y(t)) + g2(t, x(t)) = 0, t. (0, 1), n - 1 < a, beta < n; x(i)(0) = y(i)(0) = 0, i = 0, 1, 2,..., n - 2; [D. 0+ y(t)] t=1 = k1(y(1)), [D. 0+ x(t)] t=1 = k2(x(1)), where the integer number n > 3 and 1 =. =. = n - 2, 1 =. =. = n - 2, f1, f2 : [0, 1] xR+ xR+. R+, g1, g2 : [0, 1] xR+. R+ and k1, k2 : R+. R+ are continuous functions, Da0 + and D beta 0+ stand for the Riemann-Liouville derivatives. An illustrative example is given to show the effectiveness of theoretical results.Article Citation - WoS: 10Citation - Scopus: 13On a New Fixed Point Theorem With an Application on a Coupled System of Fractional Differential Equations(Springer, 2020) Abdeljawad, Thabet; Afshari, Hojjat; Jarad, FahdIn this work, new theorems and results related to fixed point theory are presented. The results obtained are used for the sake of proving the existence and uniqueness of a positive solution of a coupled system of equations that involves fractional derivatives in the Riemann-Liouville settings and is subject to boundary conditions in the form of integrals.Article Citation - WoS: 60Citation - Scopus: 65The Existence of Solutions for a Nonlinear Mixed Problem of Singular Fractional Differential Equations(Springer, 2013) Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, DumitruBy using fixed point results on cones, we study the existence of solutions for the singular nonlinear fractional boundary value problem (c)D(alpha)u(t) = f(t, u(t), u'(t), (c)D(beta)u(t)), u(0) = au(1), u'(0) = b(c)D(beta)u(1), u ''(0) = u'''(0) = u((n-1))(0) = 0, where n >= 3 is an integer, alpha is an element of (n - 1, n), 0 < beta < 1, 0 < a < 1, 0 < b < Gamma (2 - beta), f is an L-q-Caratheodory function, q > 1/alpha-1 and f(t,x,y,z) may be singular at value 0 in one dimension of its space variables x, y, z. Here, D-c stands for the Caputo fractional derivative.Article Citation - WoS: 142Citation - Scopus: 166On the Nonlinear Dynamical Systems Within the Generalized Fractional Derivatives With Mittag-Leffler Kernel(Springer, 2018) Jajarmi, Amin; Hajipour, Mojtaba; Baleanu, DumitruThe purpose of this paper is to study the existence and uniqueness of the solution of nonlinear fractional differential equations with Mittag-Leffler nonsingular kernel. Two numerical methods to solve this problem are designed, and their stability and error estimates are investigated by discretizing the convolution integral and using the Gronwall's inequality. Finally, the theoretical results are verified by using five illustrative examples.Article Citation - WoS: 68Citation - Scopus: 84Fractional Lie Group Method of the Time-Fractional Boussinesq Equation(Springer, 2015) Kadkhoda, Nematollah; Baleanu, Dumitru; Jafari, HosseinFinding the symmetries of the nonlinear fractional differential equations is a topic which has many applications in various fields of science and engineering. In this manuscript, firstly, we are interested in finding the Lie point symmetries of the time-fractional Boussinesq equation. After that, by using the infinitesimal generators, we determine their corresponding invariant solutions.Article Citation - WoS: 9Citation - Scopus: 8A Uniqueness Criterion for Fractional Differential Equations With Caputo Derivative(Springer, 2013) Mustafa, Octavian G.; O'Regan, Donal; Baleanu, DumitruWe investigate the uniqueness of solutions to an initial value problem associated with a nonlinear fractional differential equation of order alpha a(0,1). The differential operator is of Caputo type whereas the nonlinearity cannot be expressed as a Lipschitz function. Instead, the Riemann-Liouville derivative of this nonlinearity verifies a special inequality.