Browsing by Author "Alzabut, Jehad"
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Article Citation Count: Abdeljawad, T., Alzabut, J., Jarad, F. (2017). A generalized Lyapunov-type inequality in the frame of conformable derivatives. Advance in Difference Equations, 321. http://dx.doi.org/10.1186/s13662-017-1383-zA generalized Lyapunov-type inequality in the frame of conformable derivatives(Springer, 2017) Abdeljawad, Thabet; Alzabut, Jehad; Jarad, Fahd; 234808We 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.Article Citation Count: Abdeljawad, T., Alzabut, J., Baleanu, D. (2016). A generalized q-fractional Gronwall inequality and its applications to nonlinear delay q-fractional difference systems. Journal Of Inequalities Applications. http://dx.doi.org/ 10.1186/s13660-016-1181-2A generalized q-fractional Gronwall inequality and its applications to nonlinear delay q-fractional difference systems(Springer International Publishing, 2016) Abdeljawad, Thabet; Alzabut, Jehad; Baleanu, DumitruIn this paper, we state and prove a new discrete q-fractional version of the Gronwall inequality. Based on this result, a particular version expressed by means of the q-Mittag-Leffler function is provided. To apply the proposed results, we prove the uniqueness and obtain an estimate for the solutions of nonlinear delay Caputo q-fractional difference system. We examine our results by providing a numerical example.Article Citation Count: Alzabut, Jehad...et al. (2019). "A Gronwall inequality via the generalized proportional fractional derivative with applications", Journal of Inequalities and Applications.A Gronwall inequality via the generalized proportional fractional derivative with applications(Springer Open, 2019) Alzabut, Jehad; Abdeljawad, Thabet; Jarad, Fahd; Sudsutad, Weerawat; 234808In this paper, we provide a new version for the Gronwall inequality in the frame of the generalized proportional fractional derivative. Prior to the main results, we introduce the generalized proportional fractional derivative and expose some of its features. As an application, we accommodate the newly defined derivative to prove the uniqueness and obtain a bound in terms of Mittag-Leffler function for the solutions of a nonlinear delay proportional fractional system. An example is presented to demonstrate the applicability of the theory.Article Citation Count: Bozkurt, Fatma...et al. (2020). "A mathematical model of the evolution and spread of pathogenic coronaviruses from natural host to human host", Chaos Solitons & Fractals, Vol. 138.A mathematical model of the evolution and spread of pathogenic coronaviruses from natural host to human host(2020) Bozkurt, Fatma; Yousef, Ali; Baleanu, Dumitru; Alzabut, Jehad; 56389Coronaviruses are highly transmissible and are pathogenic viruses of the 21st century worldwide. In general, these viruses are originated in bats or rodents. At the same time, the transmission of the infection to the human host is caused by domestic animals that represent in the habitat the intermediate host. In this study, we review the currently collected information about coronaviruses and establish a model of differential equations with piecewise constant arguments to discuss the spread of the infection from the natural host to the intermediate, and from them to the human host, while we focus on the potential spillover of bat-borne coronaviruses. The local stability of the positive equilibrium point of the model is considered via the Linearized Stability Theorem. Besides, we discuss global stability by employing an appropriate Lyapunov function. To analyze the outbreak in early detection, we incorporate the Allee effect at time t and obtain stability conditions for the dynamical behavior. Furthermore, it is shown that the model demonstrates the Neimark-Sacker Bifurcation. Finally, we conduct numerical simulations to support the theoretical findings. (C) 2020 Elsevier Ltd. All rights reserved.Article Citation Count: Alzabut, J.O. "A Necessary and Sufficient Condition for the Existence of Periodic Solutions of Linear Impulsive Differential Equations With Distributed Delay", Discrete and Continuous Dynamical Systems- Series A, pp. 35-43, (2007).A Necessary and Sufficient Condition for the Existence of Periodic Solutions of Linear Impulsive Differential Equations With Distributed Delay(2007) Alzabut, JehadA necessary and sufficient condition is established for the existence of periodic solutions of linear impulsive differential equations with distributed delay.Book Part Citation Count: Alzabut, J.O.;, "A Stability Criterion for Delay Differential Equations With Impulse Effects", Applied Analysis and Differential Equations: Lasi, Romania, 4-9 September 2006, pp. 1-10, (2007).A Stability Criterion for Delay Differential Equations With Impulse Effects(World Scientific Publ CO PTE LTD, 2007) Alzabut, JehadIn this paper, we prove that if a delay differential equation with impulse effects of the form x’(t) = A(t)x(t) + B(t)x(t - τ), t ≠ θi, Δx(θi) = Cix(θi) + Dix(θi-j); i ∈ 2 N; verfies a Perron condition then its trivial solution is uniformly asymptotically stable.Article Citation Count: Alzabut, J., Bolat, Y., Abdeljawad, T. (2012). Almost periodic dynamics of a discrete Nicholson's blowflies model involving a linear harvesting term. Advance in Difference Equations. http://dx.doi.org/10.1186/1687-1847-2012-158Almost periodic dynamics of a discrete Nicholson's blowflies model involving a linear harvesting term(Springer International Publishing, 2012) Alzabut, Jehad; Bolat, Yaşar; Abdeljawad, ThabetWe consider a discrete Nicholson's blowflies model involving a linear harvesting term. Under appropriate assumptions, sufficient conditions are established for the existence and exponential convergence of positive almost periodic solutions of this model. To expose the effectiveness of the main theorems, we support our result by a numerical example.Article Citation Count: Alzabut, J., Abdeljawad, T. (2007). An exponential estimate for solutions of linear impulsive delay differential equations. Kuwait Journal of Science And Engineering, 34(1A), 39-56.An exponential estimate for solutions of linear impulsive delay differential equations(Academic Publication Council, 2007) Alzabut, Jehad; Abdeljawad, ThabetThis paper is concerned with linear impulsive delay differential equations with impulsive conditions allowing delays in the index of the jumps. We obtain an exponential estimate for the solutions of such types of equations. In preparation to this, we present three essential lemmas related to the adjoint equation, the representation of solutions and a bound for the fundamental matrix. Moreover, a sharper estimate is providedArticle Citation Count: Abdeljawad, T...et al. (2012). Banach contraction principle for cyclical mappings on partial metric spaces. Fixed Point Theory And Applications, 154, 1-7. http://dx.doi.org/10.1186/1687-1812-2012-154Banach contraction principle for cyclical mappings on partial metric spaces(Springer International Publishing, 2012) Abdeljawad, Thabet; Alzabut, Jehad; Mukheimer, A.; Zaidan, Y.We prove that the Banacah contraction principle proved by Matthews in 1994 on 0-complete partial metric spaces can be extended to cyclical mappings. However, the generalized contraction principle proved by (Ilic et al. in Appl. Math. Lett. 24:1326-1330, 2011) on complete partial metric spaces can not be extended for cyclical mappings. Some examples are given to illustrate our results. Moreover, our results generalize some of the results obtained by (Kirk et al. in Fixed Point Theory 4(1):79-89, 2003). An Edelstein type theorem is also extended when one of the sets in the cyclic decomposition is 0-compact.Article Citation Count: Abdeljawad, T...et al. (2013). Best proximity points for cyclical contraction mappings with 0-boundedly compact decompositions. Journal of Computational Analysis and Application, 15(4), 678-685.Best proximity points for cyclical contraction mappings with 0-boundedly compact decompositions(Eudoxus Press, 2013) Abdeljawad, Thabet; Alzabut, Jehad; Mukheimer, A.; Zaidan, Y.The existence of best proximity points for cyclical type contraction mappings is proved in the category of partial metric spaces. The concept of 0-boundedly compact is introduced and used in the cyclical decomposition. Some possible generalizations to the main results are discussed. Further, illustrative examples are given to demonstrate the effectiveness of our resultsArticle Citation Count: Jose, Sayooj Aby...et.al. (2023). "Computational dynamics of a fractional order substance addictions transfer model with Atangana-Baleanu-Caputo derivative", Mathematical Methods in the Applied Sciences, Vol.46, No.5, pp.5060-5085.Computational dynamics of a fractional order substance addictions transfer model with Atangana-Baleanu-Caputo derivative(2023) Jose, Sayooj Aby; Ramachandran, Raja; Baleanu, Dumitru; Panigoro, Hasan S.; Alzabut, Jehad; Balas, Valentina E.; 56389In this paper, the ABC fractional derivative is used to provide a mathematical model for the dynamic systems of substance addiction. The basic reproduction number is investigated, as well as the equilibrium points' stability. Using fixed point theory and nonlinear analytic techniques, we verify the theoretical results of solution existence and uniqueness for the proposed model. A numerical technique for getting the approximate solution of the suggested model is established by using the Adams type predictor-corrector rule for the ABC-fractional integral operator. There are several numerical graphs that correspond to different fractional orders. Furthermore, we present a numerical simulation for the transmission of substance addiction in two scenarios with fundamental reproduction numbers greater than and fewer than one.Article Citation Count: Saker, S.H., Alzabut, J. (2007). Existence of periodic solutions, global attractivity and oscillation of impulsive delay population model. Nonlinear Analysis-Real Wold Applications, 8(4), 1029-1039. http://dx.doi.org/10.1016/j.nonwa.2006.06.001Existence of periodic solutions, global attractivity and oscillation of impulsive delay population model(Pergamon-Elsevier Science LTD, 2007) Saker, S. H.; Alzabut, JehadIn this paper we consider the nonlinear impulsive delay population model. The main objective is to systematically study the qualitative behavior of the model including existence of periodic solutions, global attractivity and oscillation. The main oscillation results are the results of the prevalence of the mature cells about the periodic solutions and the global attractivity results are the conditions for nonexistence of dynamical diseases on the populationArticle Citation Count: Khan, Hasib...et.al. (2023). "Existence of solutions and a numerical scheme for a generalized hybrid class of n-coupled modified ABC-fractional differential equations with an application", AIMS Mathematics, Vol.8, No.3, pp.6609-6625.Existence of solutions and a numerical scheme for a generalized hybrid class of n-coupled modified ABC-fractional differential equations with an application(2023) Khan, Hasib; Alzabut, Jehad; Baleanu, Dumitru; Alobaidi, Ghada; Rehman, Mutti-Ur; 56389In this article, we investigate some necessary and sufficient conditions required for the existence of solutions for mABC-fractional differential equations (mABC-FDEs) with initial conditions; additionally, a numerical scheme based on the the Lagrange’s interpolation polynomial is established and applied to a dynamical system for the applications. We also study the uniqueness and Hyers-Ulam stability for the solutions of the presumed mABC-FDEs system. Such a system has not been studied for the mentioned mABC-operator and this work generalizes most of the results studied for the ABC operator. This study will provide a base to a large number of dynamical problems for the existence, uniqueness and numerical simulations. The results are compared with the classical results graphically to check the accuracy and applicability of the scheme.Article Citation Count: Subramanian, Muthaiah...et al. (2021). "Existence, uniqueness and stability analysis of a coupled fractional-order differential systems involving Hadamard derivatives and associated with multi-point boundary conditions", Advances in Difference Equations, Vol. 2021, No. 1.Existence, uniqueness and stability analysis of a coupled fractional-order differential systems involving Hadamard derivatives and associated with multi-point boundary conditions(2021) Subramanian, Muthaiah; Alzabut, Jehad; Baleanu, Dumitru; Samei, Mohammad Esmae; Zada, Akbar; 56389In this paper, we examine the consequences of existence, uniqueness and stability of a multi-point boundary value problem defined by a system of coupled fractional differential equations involving Hadamard derivatives. To prove the existence and uniqueness, we use the techniques of fixed point theory. Stability of Hyers-Ulam type is also discussed. Furthermore, we investigate variations of the problem in the context of different boundary conditions. The current results are verified by illustrative examples. © 2021, The Author(s).Article Citation Count: Jarad, Fahd; Abdeljawad, Thabet; Alzabut, Jehad, "Fractional proportional differences with memory", European Physical Journal-Special Topics, Vol. 226, No. 16-18, pp. 3333-3354, (2017).Fractional Proportional Differences With Memory(Springer Heidelberg, 2017) Abdeljawad, Thabet; Jarad, Fahd; Alzabut, Jehad; 234808In this paper, we formulate nabla fractional sums and differences and the discrete Laplace transform on the time scale hZ. Based on a local type h-proportional difference (without memory), we generate new types of fractional sums and differences with memory in two parameters which are generalizations to the formulated fractional sums and differences. The kernel of the newly defined generalized fractional sum and difference operators contain h-discrete exponential functions. The discrete h-Laplace transform and its convolution theorem are then used to study the newly introduced discrete fractional operators and also used to solve Cauchy linear fractional difference type problems with step 0 < h <= 1.Article Citation Count: Jarad, Fahd; Abdeljawad, Thabet; Alzabut, Jehad "Generalized fractional derivatives generated by a class of local proportional derivatives", European Physical Journal-Special Topics, Vol. 226, No. 16-18, pp. 3457-3471, (2017).Generalized Fractional Derivatives Generated By A Class of Local Proportional Derivatives(Springer Heidelberg, 2017) Jarad, Fahd; Abdeljawad, Thabet; Alzabut, Jehad; 234808Recently, Anderson and Ulness [Adv. Dyn. Syst. Appl. 10, 109 (2015)] utilized the concept of the proportional derivative controller to modify the conformable derivatives. In parallel to Anderson's work, Caputo and Fabrizio [Progr. Fract. Differ. Appl. 1, 73 (2015)] introduced a fractional derivative with exponential kernel whose corresponding fractional integral does not have a semi-group property. Inspired by the above works and based on a special case of the proportional-derivative, we generate Caputo and Riemann-Liouville generalized proportional fractional derivatives involving exponential functions in their kernels. The advantage of the newly defined derivatives which makes them distinctive is that their corresponding proportional fractional integrals possess a semi-group property and they provide undeviating generalization to the existing Caputo and Riemann-Liouville fractional derivatives and integrals. The Laplace transform of the generalized proportional fractional derivatives and integrals are calculated and used to solve Cauchy linear fractional type problems.Article Citation Count: ur Rehman, Mujeeb...et al. (2020). "Green–Haar wavelets method for generalized fractional differential equations", Advances in Difference Equations, Vol. 2020, No. 1.Green–Haar wavelets method for generalized fractional differential equations(2020) ur Rehman, Mujeeb; Baleanu, Dumitru; Alzabut, Jehad; Ismail, Muhammad; Saeed, Umer; 56389The objective of this paper is to present two numerical techniques for solving generalized fractional differential equations. We develop Haar wavelets operational matrices to approximate the solution of generalized Caputo–Katugampola fractional differential equations. Moreover, we introduce Green–Haar approach for a family of generalized fractional boundary value problems and compare the method with the classical Haar wavelets technique. In the context of error analysis, an upper bound for error is established to show the convergence of the method. Results of numerical experiments have been documented in a tabular and graphical format to elaborate the accuracy and efficiency of addressed methods. Further, we conclude that accuracy-wise Green–Haar approach is better than the conventional Haar wavelets approach as it takes less computational time compared to the Haar wavelet method. © 2020, The Author(s).Article Citation Count: Abdeljawad, Thabet...et al. (2019). "Lyapunov type inequalities via fractional proportional derivatives and application on the free zero disc of Kilbas-Saigo generalized Mittag-Leffler functions", European Physical Journal Plus, Vol. 134, No. 5.Lyapunov type inequalities via fractional proportional derivatives and application on the free zero disc of Kilbas-Saigo generalized Mittag-Leffler functions(Springer Heidelberg, 2019) Abdeljawad, Thabet; Jarad, Fahd; Mallak, Saed F.; Alzabut, Jehad; 234808In this article, we prove Lyapunov type inequalities for a nonlocal fractional derivative, called fractional proportional derivative, generated by modified conformable or proportional derivatives in both Riemann-Liuoville and Caputo senses. Further, in the Riemann-Liuoville case we prove a Lyapunov inequality for a fractional proportional weighted boundary value problem and apply it on a weighted Sturm-Liouville problem to estimate an upper bound for the free zero disk of the Kilbas-Saigo Mittag-Leffler functions of three parameters. The proven results generalize and modify previously obtained results in the literature.Article Citation Count: Abdeljawad, T...et al. (2018). Lyapunov-type inequalities for mixed non-linear forced differential equations within conformable derivatives. Journal Of Inequalities Applications, 143. http://dx.doi.org/10.1186/s13660-018-1731-xLyapunov-type inequalities for mixed non-linear forced differential equations within conformable derivatives(Springer, 2018) Abdeljawad, Thabet; Agarwal, Ravi P.; Alzabut, Jehad; Jarad, Fahd; Özbekler, Abdullah; 234808; 114439We 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 Count: Alzabut, J.O., Stamov, G.Tr., Sermutlu, E. (2010). On almost periodic solutions for an impulsive delay logarithmic population model. Mathematical And Computer Modelling, 51(5-6), 625-631. http://dx.doi.org/ 10.1016/j.mcm.2009.11.001On almost periodic solutions for an impulsive delay logarithmic population model(Pergamon-Elsevier Science LTD, 2010) Alzabut, Jehad; Stamov, G. T.; Sermutlu, Emre; 17647By employing the contraction mapping principle and applying the Gronwall-Bellman inequality, sufficient conditions are established to prove the existence and exponential stability of positive almost periodic solutions for an impulsive delay logarithmic population model. An example with its numerical simulations has been provided to demonstrate the feasibility of our results
