Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 12Citation - Scopus: 20On the Decomposition and Analysis of Novel Simultaneous Seiqr Epidemic Model(Amer inst Mathematical Sciences-aims, 2023) Palanivelu, Balaganesan; Jayaraj, Renuka; Baleanu, Dumitru; Dhandapani, Prasantha Bharathi; Umapathy, KalpanaIn this manuscript, we are proposing a new kind of modified Susceptible Exposed Infected Quarantined Recovered model (SEIQR) with some assumed data. The novelty imposed here in the study is that we are studying simultaneously SIR, SEIR, SIQR, and SEQR pandemic models with the same data unchanged as the SEIQR model. We are taking this model a step ahead by using a non-helpful transition because it was mostly skipped in the literature. All sorts of features that are essential to study the models, such as basic reproduction number, stability analysis, and numerical simulations have been examined for this modified model with other models.Article Citation - WoS: 18Citation - Scopus: 19Relationships Between the Discrete Riemann-Liouville and Liouville-Caputo Fractional Differences and Their Associated Convexity Results(Amer inst Mathematical Sciences-aims, 2022) Mohammed, Pshtiwan Othman; Srivastava, Hari Mohan; Baleanu, Dumitru; Abualrub, Marwan S.; Guirao, Juan L. G.In this study, we have presented two new alternative definitions corresponding to the basic definitions of the discrete delta and nabla fractional difference operators. These definitions and concepts help us in establishing a relationship between Riemann-Liouville and Liouville-Caputo fractional differences of higher orders for both delta and nabla operators. We then propose and analyse some convexity results for the delta and nabla fractional differences of the Riemann-Liouville type. We also derive similar results for the delta and nabla fractional differences of Liouville-Caputo type by using the proposed relationships. Finally, we have presented two examples to confirm the main theorems.Article Citation - WoS: 3Citation - Scopus: 3Simulating Systems of Ito? Sdes With Split-Step (?, ?)-Milstein Scheme(Amer inst Mathematical Sciences-aims, 2022) Torkzadeh, Leila; Baleanu, Dumitru; Nouri, Kazem; Ranjbar, HassanIn the present study, we provide a new approximation scheme for solving stochastic differential equations based on the explicit Milstein scheme. Under sufficient conditions, we prove that the split-step (alpha, beta)-Milstein scheme strongly convergence to the exact solution with order 1.0 in mean-square sense. The mean-square stability of our scheme for a linear stochastic differential equation with single and multiplicative commutative noise terms is studied. Stability analysis shows that the mean-square stability of our proposed scheme contains the mean-square stability region of the linear scalar test equation for suitable values of parameters alpha, beta. Finally, numerical examples illustrate the effectiveness of the theoretical results.Article Citation - WoS: 8Citation - Scopus: 8Positivity Analysis for the Discrete Delta Fractional Differences of the Riemann-Liouville and Liouville-Caputo Types(Amer inst Mathematical Sciences-aims, 2022) Srivastava, Hari Mohan; Baleanu, Dumitru; Elattar, Ehab E.; Hamed, Y. S.; Mohammed, Pshtiwan OthmanIn this article, we investigate some new positivity and negativity results for some families of discrete delta fractional difference operators. A basic result is an identity which will prove to be a useful tool for establishing the main results. Our first main result considers the positivity and negativity of the discrete delta fractional difference operator of the Riemann-Liouville type under two main conditions. Similar results are then obtained for the discrete delta fractional difference operator of the Liouville-Caputo type. Finally, we provide a specific example in which the chosen function becomes nonincreasing on a time set.Article Citation - WoS: 37Citation - Scopus: 36On Soliton Solutions of Fractional-Order Nonlinear Model Appears in Physical Sciences(Amer inst Mathematical Sciences-aims, 2022) Asjad, Muhammad Imran; Awrejcewicz, Jan; Muhammad, Taseer; Baleanu, Dumitru; Ullah, NaeemIn wave theory, the higher dimensional non-linear models are very important to define the physical phenomena of waves. Herein study we have built the various solitons solutions of (4+1) dimensional fractional-order Fokas equation by using two analytical techniques that is, the Sardarsubequation method and new extended hyperbolic function method. Different types of novel solitons are attained such as, singular soliton, bright soliton, dark soliton, and periodic soliton. To understand the physical behavior, we have plotted 2D and 3D graphs of some selected solutions. From results we concluded that the proposed methods are straightforward, simple, and efficient. Moreover, this paper offers a hint, how we can convert the fractional-order PDE into an ODE to acquire the exact solutions. Also, the proposed methods and results can be help to examine the advance fractional-order models which seem in optics, hydrodynamics, plasma and wave theory etc.Article Citation - WoS: 8Citation - Scopus: 8On a Novel Fuzzy Fractional Retarded Delay Epidemic Model(Amer inst Mathematical Sciences-aims, 2022) Thippan, Jayakumar; Baleanu, Dumitru; Sivakumar, Vinoth; Dhandapani, Prasantha BharathiThe traditional compartmental epidemic models such as SIR, SIRS, SEW consider mortality rate as a parameter to evaluate the population changes in susceptible, infected, recovered, and exposed. We present a modern model where population changes in mortality are also considered as the parameter. The existing models in epidemiology always construct a system of the closed medium in which they assume that new birth, as well as new death, will not be possible. But in real life, such a concept will not be assumed to not exist. From our wide observation, we find that the changing rate in every population case is notably negligible, That's why we are preferring to calculate them fractionally using FFDE. Using Lofti's fuzzy concept we are picturing the models after that we are estimating their non-integer values using three distinct methodologies LADM-4, DTM-4 for arbitrary fractional-order alpha(i), and RKM-4. At alpha(i) = 1, comparison of the estimations will be done. In addition to the simulation, works of numerical estimations, the existence of steady states, equilibrium points, and stability analysis are all done.Article Citation - WoS: 4Citation - Scopus: 4Nonlinear Wave Train in an Inhomogeneous Medium With the Fractional Theory in a Plane Self-Focusing(Amer inst Mathematical Sciences-aims, 2022) Faridi, Waqas Ali; Jhangeer, Adil; Aleem, Maryam; Yusuf, Abdullahi; Alshomrani, Ali S.; Baleanu, Dumitru; Asjad, Muhammad ImranThe aim of study is to investigate the Hirota equation which has a significant role in applied sciences, like maritime, coastal engineering, ocean, and the main source of the environmental action due to energy transportation on floating anatomical structures. The classical Hirota model has transformed into a fractional Hirota governing equation by using the space-time fractional Riemann-Liouville, time fractional Atangana-Baleanu and space-time fractional beta differential operators. The most generalized new extended direct algebraic technique is applied to obtain the solitonic patterns. The utilized scheme provided a generalized class of analytical solutions, which is presented by the trigonometric, rational, exponential and hyperbolic functions. The analytical solutions which cover almost all types of soliton are obtained with Riemann-Liouville, Atangana-Baleanu and beta fractional operator. The influence of the fractional-order parameter on the acquired solitary wave solutions is graphically studied. The two and three-dimensional graphical comparison between Riemann-Liouville, Atangana-Baleanu and beta-fractional derivatives for the solutions of the Hirota equation is displayed by considering suitable involved parametric values with the aid of Mathematica.Article Citation - WoS: 34Citation - Scopus: 39Nonlinear Higher Order Fractional Terminal Value Problems(Amer inst Mathematical Sciences-aims, 2022) Shiri, Babak; Baleanu, DumitruTerminal value problems for systems of fractional differential equations are studied with an especial focus on higher-order systems. Discretized piecewise polynomial collocation methods are used for approximating the exact solution. This leads to solving a system of nonlinear equations. For solving such a system an iterative method with a required tolerance is introduced and analyzed. The existence of a unique solution is guaranteed with the aid of the fixed point theorem. Order of convergence for the given numerical method is obtained. Numerical experiments are given to support theoretical results.Article Citation - WoS: 5Citation - Scopus: 12Non-Instantaneous Impulsive Fractional-Order Delay Differential Systems With Mittag-Leffler Kernel(Amer inst Mathematical Sciences-aims, 2022) Arjunan, Mani Mallika; Baleanu, Dumitru; Kavitha, VelusamyThe existence of fractional-order functional differential equations with non-instantaneous impulses within the Mittag-Leffler kernel is examined in this manuscript. Non-instantaneous impulses are involved in such equations and the solution semigroup is not compact in Banach spaces. We suppose that the nonlinear term fulfills a non-compactness measure criterion and a local growth constraint. We further assume that non-instantaneous impulsive functions satisfy specific Lipschitz criteria. Finally, an example is given to justify the theoretical results.Article Citation - WoS: 9Citation - Scopus: 9New Classifications of Monotonicity Investigation for Discrete Operators With Mittag-Leffler Kernel(Amer inst Mathematical Sciences-aims, 2022) Goodrich, Christopher S.; Brzo, Aram Bahroz; Baleanu, Dumitru; Hamed, Yasser S.; Mohammed, Pshtiwan OthmanThis paper deals with studying monotonicity analysis for discrete fractional operators with Mittag-Leffler in kernel. The v-monotonicity definitions, namely v-(strictly) increasing and v-(strictly) decreasing, are presented as well. By examining the basic properties of the proposed discrete fractional operators together with v-monotonicity definitions, we find that the investigated discrete fractional operators will be v(2)-(strictly) increasing or v(2)-(strictly) decreasing in certain domains of the time scale Na:= {a, a + 1, ... }. Finally, the correctness of developed theories is verified by deriving mean value theorem in discrete fractional calculus.