Browsing by Author "Alzabut, Jehad"

Now showing 1 - 19 of 19

Citation - WoS: 27
Citation - Scopus: 27
Almost Periodic Dynamics of a Discrete Nicholson's Blowflies Model Involving a Linear Harvesting Term
(Springer, 2012) Abdeljawad, Thabet; Alzabut, Jehad; Bolat, Yasar; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
We 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.
Citation - WoS: 17
Citation - Scopus: 13
Best Proximity Points for Cyclical Contraction Mappings With 0-Boundedly Compact Decompositions
(Eudoxus Press, Llc, 2013) Abdeljawad, Thabet; Abdeljawad, T.; Alzabut, J. O.; Alzabut, Jehad; Mukheimer, A.; Zaidan, Y.; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 results.
Citation - WoS: 14
Citation - Scopus: 16
Computational Dynamics of a Fractional Order Substance Addictions Transfer Model With Atangana-Baleanu Derivative
(Wiley, 2023) Baleanu, Dumitru; Panigoro, Hasan S.; Alzabut, Jehad; Balas, Valentina E.; Jose, Sayooj Aby; Ramachandran, Raja; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In 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.
Citation - WoS: 85
Citation - Scopus: 88
Existence of Solutions and a Numerical Scheme for a Generalized Hybrid Class of N-Coupled Modified Abc-Fractional Differential Equations With an Application
(Amer inst Mathematical Sciences-aims, 2023) Baleanu, Dumitru; Alobaidi, Ghada; Rehman, Mutti-Ur; Khan, Hasib; Alzabut, Jehad; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In 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.
Citation - WoS: 30
Citation - Scopus: 30
Existence, Uniqueness and Stability Analysis of a Coupled Fractional-Order Differential Systems Involving Hadamard Derivatives and Associated With Multi-Point Boundary Conditions
(Springer, 2021) Baleanu, Dumitru; Samei, Mohammad Esmael; Zada, Akbar; Subramanian, Muthaiah; Alzabut, Jehad; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In 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.
An Exponential Estimate for Solutions of Linear Impulsive Delay Differential Equations
(Academic Publication Council, 2007) Alzabut, Jehad; Alzabut, Jehad; Abdeljawad, Thabet; Abdeljawad, Thabet; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This 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 provided.
Citation - WoS: 46
Citation - Scopus: 49
Fractional Proportional Differences With Memory
(Springer Heidelberg, 2017) Abdeljawad, Thabet; Jarad, Fahd; Alzabut, Jehad; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In 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.
Citation - WoS: 255
Citation - Scopus: 277
Generalized Fractional Derivatives Generated by a Class of Local Proportional Derivatives
(Springer Heidelberg, 2017) Jarad, Fahd; Abdeljawad, Thabet; Alzabut, Jehad; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Recently, 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.
Citation - WoS: 70
Citation - Scopus: 91
A Generalized Lyapunov-Type Inequality in the Frame of Conformable Derivatives
(Springeropen, 2017) Abdeljawad, Thabet; Alzabut, Jehad; Jarad, Fahd; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
We 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.
Citation - WoS: 54
Citation - Scopus: 58
A Generalized Q-Fractional Gronwall Inequality and Its Applications To Nonlinear Delay Q-Fractional Difference Systems
(Springeropen, 2016) Abdeljawad, Thabet; Alzabut, Jehad; Baleanu, Dumitru; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In 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.
Citation - WoS: 34
Citation - Scopus: 36
Green-Haar Wavelets Method for Generalized Fractional Differential Equations
(Springer, 2020) Alzabut, Jehad; Ismail, Muhammad; Saeed, Umer; Rehman, Mujeeb Ur; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The 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.
Citation - WoS: 67
Citation - Scopus: 76
A Gronwall Inequality Via the Generalized Proportional Fractional Derivative With Applications
(Springer, 2019) Sudsutad, Weerawat; Alzabut, Jehad; Abdeljawad, Thabet; Jarad, Fahd; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In 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.
Citation - WoS: 16
Citation - Scopus: 19
Lyapunov Type Inequalities Via Fractional Proportional Derivatives and Application on the Free Zero Disc of Kilbas-Saigo Generalized Mittag-Leffler Functions
(Springer Heidelberg, 2019) Alzabut, Jehad; Abdeljawad, Thabet; Jarad, Fahd; Mallak, Saed F.; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
.In 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.
Citation - WoS: 35
Citation - Scopus: 42
Lyapunov-Type Inequalities for Mixed Non-Linear Forced Differential Equations Within Conformable Derivatives
(Springer, 2018) Jarad, Fahd; Ozbekler, Abdullah; Abdeljawad, Thabet; Agarwal, Ravi P.; Alzabut, Jehad; 234808; 114439; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 28
Citation - Scopus: 29
A Mathematical Model of the Evolution and Spread of Pathogenic Coronaviruses From Natural Host To Human Host
(Pergamon-elsevier Science Ltd, 2020) Baleanu, Dumitru; Alzabut, Jehad; Bozkurt, Fatma; Yousef, Ali; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Coronaviruses 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.
Citation - Scopus: 5
A Necessary and Sufficient Condition for the Existence of Periodic Solutions of Linear Impulsive Differential Equations With Distributed Delay
(2007) Alzabut, J.O.; Alzabut, Jehad; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
A necessary and sufficient condition is established for the existence of periodic solutions of linear impulsive differential equations with distributed delay.
Citation - Scopus: 12
On Periodic Solutions of Linear Impulsive Delay Differential Systems
(2008) Alzabut, Jehad; Akhmet, M.U.; Alzabut, J.O.; Zafer, A.; 351454; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
A necessary and sufficient condition is established for the existence of periodic solutions of linear impulsive delay differential systems. Copyright © 2008 Watam Press.
Citation - WoS: 7
Citation - Scopus: 6
Perron's Theorem for Q-Delay Difference Equations
(Natural Sciences Publishing Corp-nsp, 2011) Alzabut, Jehad; Alzabut, J. O.; Abdeljawad, T.; Abdeljawad, Thabet; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we prove that if a linear q-delay difference equation satisfies Perron's condition then its trivial solution is uniformly asymptotically stable.
Citation - WoS: 1
Citation - Scopus: 1
Recent Developments and Applications on Discrete Fractional Equations and Related Topics
(Hindawi Ltd, 2013) Alzabut, Jehad; Sun, Shurong; Abdeljawad, Thabet; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi