Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article On Multiplicative Fractional Operators of Hadamard and Katugampola Types in G-Calculus and Related Hermite-Hadamard Inequalities(World Scientific Publ Co Pte Ltd, 2026) Abdeljawad, Thabet; Lakhdari, Abdelghani; Jarad, Fahd; Budak, Hüseyin; Alqudah, Manar AThis paper explores the extension of classical fractional operators to the framework of G-calculus, a non-Newtonian calculus in which differentiation and integration are defined via multiplicative analogs of their classical counterparts. We begin by recalling key concepts from both fractional calculus and G-calculus. Next, we revisit the recently introduced multiplicative Riemann-Liouville fractional operators and extend the multiplicative Riemann-Liouville fractional derivative to arbitrary order alpha > 0. Building on this foundation, we introduce multiplicative versions of the Hadamard and Katugampola fractional integrals and derivatives. Finally, we establish Hermite-Hadamard inequalities for both newly defined integrals.Article On the Finite Delayed Fractional Differential Equation via the Weighted Riemann-Liouville Derivative of Variable Order(World Scientific Publ Co Pte Ltd, 2026) Jarad, Fahd; Abdeljawad, Thabet; Souid, Mohammed Said; Hallouz, Abdelhamid; Alqudah, ManarThis study investigates the existence and uniqueness of solutions to initial value problems for nonlinear variable-order weighted fractional differential equations with finite delay. Building upon and generalizing prior constant-order fractional models, our approach employs fixed-point theory, specifically the Banach and Schauder fixed-point theorems, in suitable weighted function spaces to rigorously establish these fundamental results. We further demonstrate the applicability of our theoretical framework through illustrative examples. The findings contribute significantly to the mathematical understanding and modeling capabilities of complex systems exhibiting memory and hereditary properties governed by variable-order fractional dynamics.Article Citation - WoS: 6Citation - Scopus: 6Modeling the Transmission Dynamics of Middle Eastern Respiratory Syndrome Coronavirus with the Impact of Media Coverage(Elsevier, 2021) Fatima, BiBi; Alqudah, Manar A.; Zaman, Gul; Jarad, Fahd; Abdeljawad, ThabetMiddle East respiratory syndrome coronavirus has been persistent in the Middle East region since 2012. In this paper, we propose a deterministic mathematical model to investigate the effect of media coverage on the transmission and control of Middle Eastern respiratory syndrome coronavirus disease. In order to do this we develop model formulation. Basic reproduction number R-0 will be calculated from the model to assess the transmissibility of the (MERS-CoV). We discuss the existence of backward bifurcation for some range of parameters. We also show stability of the model to figure out the stability condition and impact of media coverage. We show a special case of the model for which the endemic equilibrium is globally asymptotically stable. Finally all the theoretical results will be verified with the help of numerical simulation for easy understanding.Article Citation - WoS: 4Citation - Scopus: 4Fractional Vector Calculus in the Frame of a Generalized Caputo Fractional Derivative(Univ Politehnica Bucharest, Sci Bull, 2018) Jarad, Fahd; Gambo, Yusuf Ya'u; Baleanu, Dumitru; Jarad, Fahd; Baleanu, Dumitru; Abdeljawad, Thabet; Abdeljawad, Thabet; MatematikThe authors in [1] recently introduced a new generalized fractional derivative on AC(y)(n)[a ,b] and C-y(n)[a, b], and defined their Caputo version. This derivative contains two parameters and reduces to the classical Caputo derivatives if one of these parameters tend to certain values. From here and after, by generalized Caputo fractional derivative, we refer to the Caputo version of the generalized fractional derivative. This paper studies the generalized Caputo fractional derivative and establishes the Fundamental Theorem of Fractional Calculus (FTFC) in the sense of this derivative. The fundamental results are used in establishing some vital theorems and then applied to vector calculus.Article Citation - WoS: 60Citation - Scopus: 68Lyapunov-Krasovskii Stability Theorem for Fractional Systems With Delay(Editura Acad Romane, 2011) Baleanu, Dumitru; Baleanu, D.; Ranjbar N, A.; Abdeljawad, Thabet; Sadati R, S. J.; Delavari, R. H.; Abdeljawad (Maraaba), T.; Gejji, V.; MatematikFractional calculus techniques and methods started to be applied during the last decades in several fields of science and engineering. In this paper we studied the stability of fractional order nonlinear time-delay systems for Caputo's derivative and we extended Lyapunov-Krasovskii theorem for the fractional nonlinear systems.Article Citation - WoS: 14Citation - Scopus: 19On the Discrete Sumudu Transform(Editura Acad Romane, 2012) Jarad, Fahd; Jarad, Fahd; Abdeljawad, Thabet; Bayram, Kamm; Abdeljawad, Thabet; Baleanu, Dumitru; Baleanu, Dumitru; Köse, Hasan; Ameen, Raad; MatematikIn this paper, we define the Sumudu transform on an arbitrary time scale. Starting from this definition we define the discrete Sumudu transform. We prove the initial and final value problems and study the basic properties of this transform. We also present the discrete Sumudu transform of some basic functions.Article Citation - WoS: 6Citation - Scopus: 6A Caputo Fractional Order Boundary Value Problem With Integral Boundary Conditions(Eudoxus Press, Llc, 2013) Babakhani, Azizollah; Abdeljawad, Thabet; Abdeljawad, Thabet; MatematikIn this paper, we discuss existence and uniqueness of solutions to nonlinear fractional order ordinary differential equations with integral boundary conditions in an ordered Banach space. We use the Caputo fractional differential operator and the nonlinearity depends on the fractional derivative of an unknown function. The nonlinear alternative of the Leray- Schauder type Theorem is the main tool used here to establish the existence and the Banach contraction principle to show the uniqueness of the solution under certain conditions. The compactness of solutions set is also investigated and an example is included to show the applicability of our results.Article Citation - WoS: 2Citation - Scopus: 5Some Fixed Point Results in Tvs-Cone Metric Spaces(House Book Science-casa Cartii Stiinta, 2013) Abdeljawad, T.; Abdeljawad, Thabet; Rezapour, Sh; MatematikEvery TVS-cone metric space is topologically isomorphic to a topological metric space. In this paper, by using a nonlinear scalarization, we give some fixed point results with nonlinear contractive conditions on TVS-cone metric spaces.Article Citation - WoS: 3Citation - Scopus: 4A Gregus Type Common Fixed Point Theorem of Set-Valued Mappings in Cone Metric Spaces(Eudoxus Press, Llc, 2011) Abdeljawad, Thabet; Abdeljawad, T.; Murthy, P. P.; Taş, Kenan; Tas, K.; MatematikThe main purpose of this paper is to obtain a common fixed point theorem for a pair of set-valued mappings of Gregus type condition in cone metric spaces, so that the main result obtained in [13] will be generalized to cone metric spaces. The cone under consideration will be normal with normal constant K = 1.Article Citation - WoS: 38Citation - Scopus: 39On the Mittag-Leffler Stability of Q-Fractional Nonlinear Dynamical Systems(Editura Acad Romane, 2011) Jarad, Fahd; Jarad, Fahd; Abdeljawad, Thabet; Abdeljawad, Thabet; Gundogdu, Emrah; Baleanu, Dumitru; Baleanu, Dumitru; MatematikIn this article, analogous to the definition of the exponential stability of ordinary dynamical systems and the Mittag-Leffler stability of the fractional dynamical systems, we consider the Mittag-Leffler stability for q-fractional nonlinear dynamical systems. The sufficient conditions for Mittag-Leffler stability of such dynamical systems within the framework of the q-fractional Caputo derivative are studied.