Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Now showing 1 - 10 of 147
  • Article
    Citation - WoS: 12
    Citation - Scopus: 20
    On 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, Kalpana
    In 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: 6
    Citation - Scopus: 7
    Fixed Point Results in C*-Algebra Bipolar Metric Spaces With an Application
    (Amer inst Mathematical Sciences-aims, 2023) Gnanaprakasam, Arul Joseph; Isik, Huseyin; Jarad, Fahd; Mani, Gunaseelan
    In this work, we prove existence and uniqueness fixed point theorems under Banach and Kannan type contractions on C*-algebra-valued bipolar metric spaces. To strengthen our main results, an appropriate example and an effective application are presented.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 6
    Existence and Ulam-Hyers Stability of Mild Solutions for Impulsive Integro-Differential Systems Via Resolvent Operators
    (Amer inst Mathematical Sciences-aims, 2025) Salim, Abdelkrim; Benchohra, Mouffak; Karapinar, Erdal; Bensalem, Abdelhamid
    The aim of this paper is to present existence, Ulam-Hyers-Rassias stability and continuous dependence on initial conditions for the mild solution of impulsive integro-differential systems via resolvent operators. Our analysis is based on fixed point theorem with generalized measures of noncompactness, this approach is combined with the technique that uses convergence to zero matrices in generalized Banach spaces. An example is presented to illustrate the efficiency of the result obtained.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 6
    An Inevitable Note on Bipolar Metric Spaces
    (Amer inst Mathematical Sciences-aims, 2024) Cvetkovic, Marija; Karapinar, Erdal
    Bipolar metric spaces and related fixed point theorems therein were introduced based on the motivation of measuring the distance between the elements of distinct sets. The question regarding the independence of these results from the analogous results on a fixed point of an induced mapping on a Cartesian product of two sets. We proved that bipolar metric space is metrizable and we presented two different approaches for defining a metric induced by a bipolar metric. Two obtained metric spaces demonstrated the lack of novelty of fixed point theorems for covariant and contravariant contraction.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 2
    Some Qualitative Properties of Solutions To a Nonlinear Fractional Differential Equation Involving Two Φ-Caputo Fractional Derivatives
    (Amer inst Mathematical Sciences-aims, 2022) Al-Mdallal, Qasem M.; Jarad, Fahd; Baitiche, Zidane; Derbazi, Choukri
    The momentous objective of this work is to discuss some qualitative properties of solutions such as the estimate of the solutions, the continuous dependence of the solutions on initial conditions and the existence and uniqueness of extremal solutions to a new class of fractional differential equations involving two fractional derivatives in the sense of Caputo fractional derivative with respect to another function Phi. Firstly, using the generalized Laplace transform method, we give an explicit formula of the solutions to the aforementioned linear problem which can be regarded as a novelty item. Secondly, by the implementation of the Phi-fractional Gronwall inequality, we analyze some properties such as estimates and continuous dependence of the solutions on initial conditions. Thirdly, with the help of features of the Mittag-Leffler functions (MLFs), we build a new comparison principle for the corresponding linear equation. This outcome plays a vital role in the forthcoming analysis of this paper especially when we combine it with the monotone iterative technique alongside facet with the method of upper and lower solutions to get the extremal solutions for the analyzed problem. Lastly, we present some examples to support the validity of our main results.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 2
    Solving a Fredholm Integral Equation Via Coupled Fixed Point on Bicomplex Partial Metric Space
    (Amer inst Mathematical Sciences-aims, 2022) Gnanaprakasam, Arul Joseph; Javed, Khalil; Arshad, Muhammad; Jarad, Fahd; Mani, Gunaseelan
    In this paper, we obtain some coupled fixed point theorems on a bicomplex partial metric space. An example and an application to support our result are presented.
  • Article
    Citation - WoS: 18
    Citation - Scopus: 19
    Relationships 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: 6
    Citation - Scopus: 8
    Unsteady Casson Fluid Flow Over a Vertical Surface With Fractional Bioconvection
    (Amer inst Mathematical Sciences-aims, 2022) Butt, Muhammad Haris; Sadiq, Muhammad Armaghan; Ikram, Muhammad Danish; Jarad, Fahd; Asjad, Muhammad Imran
    This paper deals with unsteady flow of fractional Casson fluid in the existence of bioconvection. The governing equations are modeled with fractional derivative which is transformed into dimensionless form by using dimensionless variables. The analytical solution is attained by applying Laplace transform technique. Some graphs are made for involved parameters. As a result, it is found that temperature, bioconvection are maximum away from the plate for large time and vice versa and showing dual behavior in their boundary layers respectively. Further recent literature is recovered from the present results and obtained good agreement.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    Simulating Systems of Ito? Sdes With Split-Step (?, ?)-Milstein Scheme
    (Amer inst Mathematical Sciences-aims, 2022) Torkzadeh, Leila; Baleanu, Dumitru; Nouri, Kazem; Ranjbar, Hassan
    In 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: 8
    Citation - Scopus: 8
    Qualitative Analysis of a Fuzzy Volterra-Fredholm Integrodifferential Equation With an Atangana-Baleanu Fractional Derivative
    (Amer inst Mathematical Sciences-aims, 2022) Shah, Kamal; Jarad, Fahd; Abdo, Mohammed S.; Abdeljawad, Thabet; Almalahi, Mohammed A.; Panchal, Satish K.
    The point of this work was to analyze and investigate the sufficient conditions of the existence and uniqueness of solutions for the nonlinear fuzzy fractional Volterra Fredholm integrodifferential equation in the frame of the Atangana-Baleanu-Caputo fractional derivative methodology. To begin with, we give the parametric interval form of the Atangana-Baleanu-Caputo fractional derivative on fuzzy set-valued functions. Then, by employing Schauder???s and Banach???s fixed point procedures, we examine the existence and uniqueness of solutions for fuzzy fractional Volterra Fredholm integro-differential equation with the Atangana-Baleanu-Caputo fractional operator. It turns out that the last interval model is a combined arrangement of nonlinear equations. In addition, we consider results by applying the Adams Bashforth fractional technique and present two examples that have been numerically solved using graphs.