WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 4Citation - Scopus: 4Nonlinear Singular P-Laplacian Boundary Value Problems in the Frame of Conformable Derivative(Amer inst Mathematical Sciences-aims, 2021) Jarad, Fahd; Adjabi, Yassine; Abdeljawad, Thabet; Bouloudene, Mokhtar; Alqudah, Manar A.This paper studies a class of fourth point singular boundary value problem of p-Laplacian operator in the setting of a specific kind of conformable derivatives. By using the upper and lower solutions method and fixed point theorems on cones., necessary and sufficient conditions for the existence of positive solutions are obtained. In addition, we investigate the dependence of the solution on the order of the conformable differential equation and on the initial conditions.Article Citation - WoS: 12Citation - Scopus: 13On Defining the Distributions Δ<sup>r</Sup> and (δ′)<sup>r</Sup> by Conformable Derivatives(Springeropen, 2018) Abdeljawad, Thabet; Jarad, Fahd; Adjabi, Yassine; Baleanu, DumitruIn this paper, starting from a fixed delta-sequence, we use the generalized Taylor's formula based on conformable derivatives and the neutrix limit to find the powers of the Dirac delta function delta(r) and (delta')(r) for any r is an element of R.Article Citation - WoS: 36Citation - Scopus: 44Lyapunov-Type Inequalities for Mixed Non-Linear Forced Differential Equations Within Conformable Derivatives(Springer, 2018) Jarad, Fahd; Ozbekler, Abdullah; Abdeljawad, Thabet; Agarwal, Ravi P.; Alzabut, JehadWe 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.Article Citation - WoS: 71Citation - Scopus: 94A Generalized Lyapunov-Type Inequality in the Frame of Conformable Derivatives(Springeropen, 2017) Abdeljawad, Thabet; Alzabut, Jehad; Jarad, FahdWe prove a generalized Lyapunov-type inequality for a conformable boundary value problem (BVP) of order alpha is an element of (1, 2]. Indeed, it is shown that if the boundary value problem (T(alpha)(c)x)(t) + r(t) x(t) = 0, t is an element of (c, d), x(c) = x(d) = 0 has a nontrivial solution, where r is a real-valued continuous function on [c, d], then integral(d)(c) vertical bar r(t)vertical bar dt > alpha(alpha)/(alpha - 1)(alpha-1) (d - c)(a-1). (1) Moreover, a Lyapunov type inequality of the form integral(d)(c)vertical bar r(t)vertical bar dt > 3 alpha - 1/(d - c)(2 alpha-1) (3 alpha - 1/2 alpha - 1)(2 alpha-1/a), 1/2 < alpha <= 1, (2) is obtained for a sequential conformable BVP. Some examples are given and an application to conformable Sturm-Liouville eigenvalue problem is analyzed.