Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 34Citation - Scopus: 35On Well-Posedness of the Sub-Diffusion Equation With Conformable Derivative Model(Elsevier, 2020) Tran Bao Ngoc; Baleanu, Dumitru; O'Regan, Donal; Nguyen Huy Tuan; Ngoc, Tran Bao; Tuan, Nguyen HuyIn this paper, we study an initial value problem for the time diffusion equation (C)partial derivative(beta)/partial derivative t(beta) u + Au = F, 0 < beta <= 1, on Omega x (0, T), where the time derivative is the conformable derivative. We study the existence and regularity of mild solutions in the following three cases with source term F: F = F (x, t), i.e., linear source term; F = F (u) is nonlinear, globally Lipchitz and uniformly bounded. The results in this case play important roles in numerical analysis. F = F (u) is nonlinear, locally Lipchitz and uniformly bounded. The analysis in this case can be widely applied to many problems such as - Time Ginzburg-Landau equations C partial derivative(beta)u/partial derivative t(beta)+ (-Delta)u = vertical bar u vertical bar(mu-1) u; - Time Burgers equations C partial derivative(beta)u/partial derivative t(beta)-( u center dot del) u + (- Delta)u = 0; etc. (C) 2020 Elsevier B.V. All rights reserved.Article Citation - Scopus: 6Computational Solutions of Conformable Space-Time Derivatives Dynamical Wave Equations: Analytical Mathematical Techniques(Elsevier B.V., 2020) Seadawy, A.R.; Baleanu, D.; Ali, A.In this article, the instigator sets up the profuse traveling wave solutions four types of fractional nonlinear equations in the sense of conformable derivatives by using the novel form of modified mathematical technique. The constructed traveling wave solutions are articulated in terms of trigonometric, hyperbolic and exponential functions. The derived results are fruitful for the physical demonstrations of problems in mathematical physics and engineering. © 2020 The AuthorsArticle Citation - WoS: 27Citation - Scopus: 31Soliton Structures To Some Time-Fractional Nonlinear Differential Equations With Conformable Derivative(Springer, 2018) Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru; Inc, MustafaThis research presents new soliton structures to some time-fractional nonlinear differential equations (TFNDEs) with conformable derivative. The powerful Ricatti-Bernoulli (RB) sub-ODE method is used to carry out the soliton solutions. Some of the obtained solutions include trigonometric, periodic wave and hyperbolic solutions. The constraint conditions for the existence of solitons are also presented. The RB sub-ODE method proves to be efficient and effective for the extraction of soliton structures for different types of TFNDEs. Some interesting figures for the numerical simulation of the obtained results are presented.Article Citation - WoS: 46Citation - Scopus: 52Physical Properties of the Projectile Motion Using the Conformable Derivative(Elsevier, 2019) Baleanu, Dumitru; Ebaid, Abdelhalim; Alharbi, Fahad M.In this paper, the projectile motion in a resisting medium has been investigated by using the conformable derivative. In order to preserve the dimensionality of the physical quantities, an auxiliary parameter sigma, which has a dimension of seconds, was imposed in the fractional derivative. The converted FDEs have been analytically solved. In the literature, some authors have suggested some relations between the auxiliary parameter sigma and the resistant parameter k. Their procedure is a special case in view of the current results. So, it has been proved in this paper that the dimensions of the physical quantities are always correct without any further assumptions that relate sigma with k. Moreover, it is shown in this paper that the fractional order has no effect neither on the trajectory nor on the range of the projectile, i.e., unlike the corresponding previous results. However, the flight time of the projectile depends on the non-integer order a of the conformable derivative. The impacts of the involved parameters on the projectile properties are discussed through tables and several graphs. The values of the range and the flight time are tabulated for the purpose of comparisons with a previous work in the literature and also with the experimental data. Hence, we give some light on the difference between the conformable derivative and the other definitions when applied on the projectile problem.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: 45Citation - Scopus: 52New Solutions for Conformable Fractional Nizhnik-Novikov System Via G'/g Expansion Method and Homotopy Analysis Methods(Springer, 2017) Tasbozan, O.; Baleanu, D.; Kurt, A.The main purpose of this paper is to find the exact and approximate analytical solution of Nizhnik-Novikov-Veselov system which may be considered as a model for an incompressible fluid with newly defined conformable derivative by using G'/G expansion method and homotopy analysis method (HAM) respectively. Authors used conformable derivative because of its applicability and lucidity. It is known that, the NNV system of equations is an isotropic Lax integrable extension of the well-known KdV equation and has physical significance. Also, NNV system of equations can be derived from the inner parameter-dependent symmetry constraint of the KP equation. Then the exact solutions obtained by using G'/G expansion method are compared with the approximate analytical solutions attained by employing HAM.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.