Browsing by Author "Alzabut, Jehad"

Now showing 1 - 7 of 7

Citation - WoS: 2
Citation - Scopus: 3
Lyapunov and Hartman-Type Inequalities for Higher-Order Discrete Fractional Boundary Value Problems
(Univ Miskolc inst Math, 2023) Oguz, Arzu Denk; Alzabut, Jehad; Ozbekler, Abdullah; Jonnalagadda, Jagan Mohan
By employing Green's function, we obtain new Lyapunov and Hartman-type inequalities for higher-order discrete fractional boundary value problems. Reported results essentially generalize some theorems existing in the literature. As an application, we discuss the corresponding eigenvalue problems.
Citation - WoS: 35
Citation - Scopus: 43
Lyapunov-Type Inequalities for Mixed Non-Linear Forced Differential Equations Within Conformable Derivatives
(Springer, 2018) Abdeljawad, Thabet; Agarwal, Ravi P.; Alzabut, Jehad; Jarad, Fahd; Ozbekler, Abdullah
We state and prove new generalized Lyapunov-type and Hartman-type inequalities fora conformable boundary value problem of order alpha is an element of (1,2] with mixed non-linearities of the form ((T alpha X)-X-a)(t) + r(1)(t)vertical bar X(t)vertical bar(eta-1) X(t) + r(2)(t)vertical bar x(t)vertical bar(delta-1) X(t) = g(t), t is an element of (a, b), satisfying the Dirichlet boundary conditions x(a) = x(b) = 0, where r(1), r(2), and g are real-valued integrable functions, and the non-linearities satisfy the conditions 0 < eta < 1 < delta < 2. Moreover, Lyapunov-type and Hartman-type inequalities are obtained when the conformable derivative T-alpha(a) is replaced by a sequential conformable derivative T-alpha(a) circle T-alpha(a), alpha is an element of (1/2,1]. The potential functions r(1), r(2) as well as the forcing term g require no sign restrictions. The obtained inequalities generalize some existing results in the literature.
Citation - WoS: 4
New Criteria on Oscillatory and Asymptotic Behavior of Third-Order Nonlinear Dynamic Equations With Nonlinear Neutral Terms
(Mdpi, 2021) Grace, Said R.; Alzabut, Jehad; Ozbekler, Abdullah
In the paper, we provide sufficient conditions for the oscillatory and asymptotic behavior of a new type of third-order nonlinear dynamic equations with mixed nonlinear neutral terms. Our theorems not only improve and extend existing theorems in the literature but also provide a new approach as far as the nonlinear neutral terms are concerned. The main results are illustrated by some particular examples.
Citation - WoS: 4
Citation - Scopus: 6
On the Oscillation of Even-Order Nonlinear Differential Equations With Mixed Neutral Terms
(Hindawi Ltd, 2021) Kaabar, Mohammed K. A.; Özbekler, Abdullah; Grace, Said R.; Alzabut, Jehad; Ozbekler, Abdullah; Siri, Zailan; Özbekler, Abdullah; Mathematics; Mathematics
The oscillation of even-order nonlinear differential equations (NLDiffEqs) with mixed nonlinear neutral terms (MNLNTs) is investigated in this work. New oscillation criteria are obtained which improve, extend, and simplify the existing ones in other previous works. Some examples are also given to illustrate the validity and potentiality of our results.
Citation - WoS: 9
Citation - Scopus: 13
On the Oscillation of Non-Linear Fractional Difference Equations With Damping
(Mdpi, 2019) Alzabut, Jehad; Muthulakshmi, Velu; Ozbekler, Abdullah; Adigilzel, Hakan
In studying the Riccati transformation technique, some mathematical inequalities and comparison results, we establish new oscillation criteria for a non-linear fractional difference equation with damping term. Preliminary details including notations, definitions and essential lemmas on discrete fractional calculus are furnished before proceeding to the main results. The consistency of the proposed results is demonstrated by presenting some numerical examples. We end the paper with a concluding remark.
Citation - WoS: 3
Citation - Scopus: 3
Oscillation Criteria for Non-Canonical Second-Order Nonlinear Delay Difference Equations With a Superlinear Neutral Term
(Texas State Univ, 2023) Vidhyaa, Kumar S.; Thandapani, Ethiraju; Alzabut, Jehad; Ozbekler, Abdullah
We obtain oscillation conditions for non-canonical second-order nonlinear delay difference equations with a superlinear neutral term. To cope with non-canonical types of equations, we propose new oscillation criteria for the main equation when the neutral coefficient does not satisfy any of the conditions that call it to either converge to 0 or & INFIN;. Our approach differs from others in that we first turn into the non-canonical equation to a canonical form and as a result, we only require one condition to weed out non-oscillatory solutions in order to induce oscillation. The conclusions made here are new and have been condensed significantly from those found in the literature. For the sake of confirmation, we provide examples that cannot be included in earlier works.
Citation - WoS: 1
Citation - Scopus: 2
Oscillation Results for a Class of Nonlinear Fractional Order Difference Equations with Damping Term
(Hindawi Ltd, 2020) Selvam, A. George Maria; Alzabut, Jehad; Jacintha, Mary; Ozbekler, Abdullah
The paper studies the oscillation of a class of nonlinear fractional order difference equations with damping term of the form Delta[psi(lambda)z(eta) (lambda)] + p(lambda)z(eta) (lambda) + q(lambda)F(Sigma(lambda-1+mu)(s=lambda 0) (lambda - s - 1)((-mu)) y(s)) = , where z(lambda) = a(lambda) + b(lambda)Delta(mu) y(lambda), Delta(mu) stands for the fractional difference operator in Riemann-Liouville settings and of order mu, 0 < mu <= 1, and eta >= 1 is a quotient of odd positive integers and lambda is an element of N lambda 0+1-mu. New oscillation results are established by the help of certain inequalities, features of fractional operators, and the generalized Riccati technique. We verify the theoretical outcomes by presenting two numerical examples.