Özbekler, Abdullah

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Profile URL
https://hdl.handle.net/20.500.14411/7654
Name Variants
Abdullah, Özbekler
A., Ozbekler
Ozbekler, Abdullah
O., Abdullah
O.,Abdullah
Abdullah, Ozbekler
A.,Ozbekler
Ozbekler,A.
Ö.,Abdullah
Özbekler,A.
A.,Özbekler
Özbekler, Abdullah
Ozbekler, A.
Oezbekler, A.
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Profesör Doktor
Email Address
abdullah.ozbekler@atilim.edu.tr
Main Affiliation
Mathematics
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Former Staff
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Scholarly Output

42

Articles

39

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112/0

Supervised MSc Theses

0

Supervised PhD Theses

0

WoS Citation Count

272

Scopus Citation Count

338

WoS h-index

10

Scopus h-index

11

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0

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0

WoS Citations per Publication

6.48

Scopus Citations per Publication

8.05

Open Access Source

15

Supervised Theses

0

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JournalCount
Mathematical Methods in the Applied Sciences6
Applied Mathematics and Computation4
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas3
Journal of Function Spaces2
Applied Mathematics Letters2
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2015 - 20209
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Author: Agarwal, Ravi P.Has files: false

Scholarly Output Search Results

Now showing 1 - 9 of 9
  • Thumbnail Image
    Article
    Citation - WoS: 16
    Citation - Scopus: 16
    Lyapunov Type Inequalities for Even Order Differential Equations With Mixed Nonlinearities
    (Springeropen, 2015) Agarwal, Ravi P.; Ozbekler, Abdullah
    In the case of oscillatory potentials, we present Lyapunov and Hartman type inequalities for even order differential equations with mixed nonlinearities: x((2n))(t) + (-1)(n-1) Sigma(m)(i=1) q(i)(t)vertical bar x(t)vertical bar(alpha i-1) x(t) = 0, where n,m epsilon N and the nonlinearities satisfy 0 < alpha(1) < center dot center dot center dot < alpha(j) < 1 < alpha(j+1) < center dot center dot center dot < alpha(m) < 2.
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    Article
    Citation - WoS: 35
    Citation - Scopus: 44
    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.
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    Article
    Citation - WoS: 9
    Citation - Scopus: 10
    Lyapunov Type Inequalities for Nth Order Forced Differential Equations With Mixed Nonlinearities
    (Amer inst Mathematical Sciences-aims, 2016) Agarwal, Ravi P.; Ozbekler, Abdullah
    In the case of oscillatory potentials, we present Lyapunov type inequalities for nth order forced differential equations of the form x((n))(t) + Sigma(m)(j=1) qj (t)vertical bar x(t)vertical bar(alpha j-1)x(t)= f(t) satisfying the boundary conditions x(a(i)) = x(1)(a(i)) = x(11)(ai) = center dot center dot center dot = x((ki))(ai) = 0; i = 1, 2,..., r, where a(1) < a(2) < ... < a(r), 0 <= k(i) and Sigma(r)(j=1) k(j) + r = n: r >= 2. No sign restriction is imposed on the forcing term and the nonlinearities satisfy 0 < alpha(l) < ... < alpha a(j) < 1 < alpha a(j+1) < ... < alpha(m) < 2. The obtained inequalities generalize and compliment the existing results in the literature.
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    Article
    Citation - WoS: 3
    Citation - Scopus: 3
    Lyapunov type inequalities for second-order forced dynamic equations with mixed nonlinearities on time scales
    (Springer-verlag Italia Srl, 2017) Agarwal, Ravi P.; Cetin, Erbil; Ozbekler, Abdullah
    In this paper, we present some newHartman and Lyapunov inequalities for second-order forced dynamic equations on time scales T with mixed nonlinearities: x(Delta Delta)(t) + Sigma(n)(k=1) qk (t)vertical bar x(sigma) (t)vertical bar (alpha k-1) x(sigma) (t) = f (t); t is an element of [t(0), infinity)(T), where the nonlinearities satisfy 0 < alpha(1) < ... < alpha(m) < 1 < alpha(m+1) < ... < alpha(n) < 2. No sign restrictions are imposed on the potentials qk, k = 1, 2, ... , n, and the forcing term f. The inequalities obtained generalize and compliment the existing results for the special cases of this equation in the literature.
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    Review
    Citation - WoS: 3
    Citation - Scopus: 3
    Lyapunov Type Inequalities for Second Order Forced Mixed Nonlinear Impulsive Differential Equations
    (Elsevier Science inc, 2016) Agarwal, Ravi P.; Ozbekler, Abdullah
    In this paper, we present some new Lyapunov and Hartman type inequalities for second order forced impulsive differential equations with mixed nonlinearities: x ''(t) + p(t)vertical bar x(t)vertical bar(beta-1)x(t) + q(t)vertical bar x(t)vertical bar(gamma-1)x(t) = f(t), t not equal theta(i); Delta x'(t) + p(i)vertical bar x(t)vertical bar(beta-1)x(t) + q(i)vertical bar x(t)vertical bar(gamma-1) x(t) = f(i), t = theta(i), where p, q, f are real-valued functions, {p(i)}, {q(i)}, {f(i)} are real sequences and 0 < gamma < 1 < beta < 2. No sign restrictions are imposed on the potential functions p, q and the forcing term f and the sequences {p(i)}, {q(i)}, {f(i)}. The inequalities obtained generalize and complement the existing results for the special cases of this equation in the literature. (C) 2016 Elsevier Inc. All rights reserved.
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    Article
    Citation - WoS: 19
    Citation - Scopus: 21
    Lyapunov Type Inequalities for Mixed Nonlinear Riemann-Liouville Fractional Differential Equations With a Forcing Term
    (Elsevier, 2017) Agarwal, Ravi P.; Ozbekler, Abdullah
    In this paper, we present some new Lyapunov and Hartman type inequalities for Riemann-Liouville fractional differential equations of the form ((a)D(alpha)x)(t) + p(t) vertical bar x(t) vertical bar(mu-1) x(t) + q(t) vertical bar x(t) vertical bar(gamma-1) x(t) = f(t), where p, q, f are real-valued functions and 0 < gamma < 1 < mu < 2. No sign restrictions are imposed on the potential functions p, q and the forcing term f. The inequalities obtained generalize and compliment the existing results for the special cases of this equation in the literature. (C) 2016 Elsevier B.V. All rights reserved.
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    Article
    Citation - WoS: 2
    Citation - Scopus: 3
    Lyapunov-Type Inequalities for Lidstone Boundary Value Problems on Time Scales
    (Springer-verlag Italia Srl, 2020) Agarwal, Ravi P.; Oguz, Arzu Denk; Ozbekler, Abdullah
    In this paper, we establish new Hartman and Lyapunov-type inequalities for even-order dynamic equations x.2n (t) + (-1)n-1q(t) xs (t) = 0 on time scales T satisfying the Lidstone boundary conditions x.2i (t1) = x.2i (t2) = 0; t1, t2. [t0,8) T for i = 0, 1,..., n - 1. The inequalities obtained generalize and complement the existing results in the literature.
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    Article
    Citation - WoS: 15
    Citation - Scopus: 16
    Disconjugacy Via Lyapunov and Vallee-Poussin Type Inequalities for Forced Differential Equations
    (Elsevier Science inc, 2015) Agarwal, Ravi P.; Ozbekler, Abdullah
    In the case of oscillatory potentials, we present some new Lyapunov and Vallee-Poussin type inequalities for second order forced differential equations. No sign restriction is imposed on the forcing term. The obtained inequalities generalize and compliment the existing results in the literature. (C) 2015 Elsevier Inc. All rights reserved.
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    Article
    Citation - WoS: 6
    Citation - Scopus: 6
    Lyapunov Type Inequalities for Second Order Sub and Super-Half Differential Equations
    (Dynamic Publishers, inc, 2015) Agarwal, Ravi P.; Ozbekler, Abdullah; Mathematics
    In the case of oscillatory potential, we present a Lyapunov type inequality for second order differential equations of the form (r(t)Phi(beta)(x'(t)))' + q(t)Phi(gamma)(x(t)) = 0, in the sub-half-linear (0 < gamma < beta) and the super-half-linear (0 < beta < gamma < 2 beta) cases where Phi(*)(s) = vertical bar s vertical bar*(-1)s.