Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 56Citation - Scopus: 67On Hilfer Generalized Proportional Fractional Derivative(Springer, 2020) Kumam, Poom; Jarad, Fahd; Borisut, Piyachat; Jirakitpuwapat, Wachirapong; Ahmed, IdrisMotivated 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: 19Citation - Scopus: 24A 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: 66Citation - Scopus: 76Existence 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, AshishIn 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: 45Citation - Scopus: 53Existence Criterion for the Solutions of Fractional Order P-Laplacian Boundary Value Problems(Springer, 2015) Baleanu, Dumitru; Khan, Hasib; Khan, Rahmat Ali; Khan, Aziz; Jafari, HosseinThe 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.