Matematik Bölümü Yayın Koleksiyonu

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

Browse

Filters

2015 - 2019482020 - 202396

Settings

Publication Index: search.filters.publicationIndex.ScopusPublisher: search.filters.publisher.Mdpi

Search Results

Now showing 1 - 10 of 144
  • Editorial
    Citation - WoS: 5
    Citation - Scopus: 5
    Preface To the Special Issue "a Themed Issue on Mathematical Inequalities, Analytic Combinatorics and Related Topics in Honor of Professor Feng Qi
    (Mdpi, 2023) Du, Wei-Shih; Agarwal, Ravi Prakash; Karapinar, Erdal; Kostic, Marko; Cao, Jian
  • Article
    Some Generalizations of Novel (Δ Backward Difference )<sup>δ</Sup>-gronwall-pachpatte Dynamic Inequalities on Time Scales With Applications
    (Mdpi, 2022) Baleanu, Dumitru; El-Deeb, Ahmed A.
    We established several novel inequalities of Gronwall-Pachpatte type on time scales. Our results can be used as handy tools to study the qualitative and quantitative properties of the solutions of the initial boundary value problem for a partial delay dynamic equation. The Leibniz integral rule on time scales has been used in the technique of our proof. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities.
  • Article
    Second-Order Multiparameter Problems Containing Complex Potentials
    (Mdpi, 2022) Ugurlu, Ekin; Erdal, Ibrahim
    In this work, we provide some lower bounds for the number of squarly integrable solutions of some second-order multiparameter differential equations. To obtain the results, we use both Sims and Sleeman's ideas and the results are some generalization of the known results. To be more precise, we firstly construct the Weyl-Sims theory for the singular second-order differential equation with several spectral parameters. Then, we obtain some results for the several singular second-order differential equations with several spectral parameters.
  • Article
    The Hausdorff-Pompeiu Distance in Gn-Menger Fractal Spaces
    (Mdpi, 2022) Saadati, Reza; Li, Chenkuan; Jarad, Fahd; O'Regan, Donal; O’Regan, Donal
    This paper introduces a complete Gn-Menger space and defines the Hausdorff-Pompeiu distance in the space. Furthermore, we show a novel fixed-point theorem for Gn-Menger-theta-contractions in fractal spaces.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 5
    On Transformation Involving Basic Analogue To the Aleph-Function of Two Variables
    (Mdpi, 2022) Baleanu, Dumitru; Ayant, Frederic; Suedland, Norbert; Kumar, Dinesh; Südland, Norbert
    In our work, we derived the fractional order q-integrals and q-derivatives concerning a basic analogue to the Aleph-function of two variables (AFTV). We discussed a related application and the q-extension of the corresponding Leibniz rule. Finally, we presented two corollaries concerning the basic analogue to the I-function of two variables and the basic analogue to the Aleph-function of one variable.
  • Article
    Citation - WoS: 19
    Citation - Scopus: 23
    On the Solvability of Mixed-Type Fractional-Order Non-Linear Functional Integral Equations in the Banach Space C(I)
    (Mdpi, 2022) Mishra, Lakshmi Narayan; Mishra, Vishnu Narayan; Baleanu, Dumitru; Pathak, Vijai Kumar
    This paper is concerned with the existence of the solution to mixed-type non-linear fractional functional integral equations involving generalized proportional (kappa,phi)-Riemann-Liouville along with Erdelyi-Kober fractional operators on a Banach space C([1,T]) arising in biological population dynamics. The key findings of the article are based on theoretical concepts pertaining to the fractional calculus and the Hausdorff measure of non-compactness (MNC). To obtain this goal, we employ Darbo's fixed-point theorem (DFPT) in the Banach space. In addition, we provide two numerical examples to demonstrate the applicability of our findings to the theory of fractional integral equations.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 1
    On Some Generalizations of Integral Inequalities in N Independent Variables and Their Applications
    (Mdpi, 2022) El-Deeb, Ahmed A.; Baleanu, Dumitru; Abuelela, Waleed
    Throughout this article, generalizations of some Gronwall-Bellman integral inequalities for two real-valued unknown functions in n independent variables are introduced. We are looking at some novel explicit bounds of a particular class of Young and Pachpatte integral inequalities. The results in this paper can be utilized as a useful way to investigate the uniqueness, boundedness, continuousness, dependence and stability of nonlinear hyperbolic partial integro-differential equations. To highlight our research advantages, several implementations of these findings will be presented. Young's method, which depends on a Riemann method, will follow to prove the key results. Symmetry plays an essential role in determining the correct methods for solving dynamic inequalities.
  • Article
    Citation - WoS: 1
    On Some Important Class of Dynamic Hilbert's-type Inequalities on Time Scales
    (Mdpi, 2022) El-Deeb, Ahmed A.; Makharesh, Samer D.; Baleanu, Dumitru; Cesarano, Clemente; El-Owaidy, Hassan M.
    In this important work, we discuss some novel Hilbert-type dynamic inequalities on time scales. The inequalities investigated here generalize several known dynamic inequalities on time scales and unify and extend some continuous inequalities and their corresponding discrete analogues. Our results will be proved by using some algebraic inequalities, Holder inequality, and Jensen's inequality on time scales.
  • Article
    Citation - WoS: 27
    Citation - Scopus: 28
    On Dynamic Systems in the Frame of Singular Function Dependent Kernel Fractional Derivatives
    (Mdpi, 2019) Jarad, Fahd; Sene, Ndolane; Abdeljawad, Thabet; Madjidi, Fadila
    In this article, we discuss the existence and uniqueness theorem for differential equations in the frame of Caputo fractional derivatives with a singular function dependent kernel. We discuss the Mittag-Leffler bounds of these solutions. Using successive approximation, we find a formula for the solution of a special case. Then, using a modified Laplace transform and the Lyapunov direct method, we prove the Mittag-Leffler stability of the considered system.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 4
    On a Fractional Parabolic Equation With Regularized Hyper-Bessel Operator and Exponential Nonlinearities
    (Mdpi, 2022) Ho Duy Binh; Anh Tuan Nguyen; Baleanu, Dumitru; Binh, Ho Duy; Nguyen, Anh Tuan
    Recent decades have witnessed the emergence of interesting models of fractional partial differential equations. In the current work, a class of parabolic equations with regularized Hyper-Bessel derivative and the exponential source is investigated. More specifically, we examine the existence and uniqueness of mild solutions in Hilbert scale-spaces which are constructed by a uniformly elliptic symmetry operator on a smooth bounded domain. Our main argument is based on the Banach principle argument. In order to achieve the necessary and sufficient requirements of this argument, we have smoothly combined the application of the Fourier series supportively represented by Mittag-Leffler functions, with Hilbert spaces and Sobolev embeddings. Because of the presence of the fractional operator, we face many challenges in handling proper integrals which appear in the representation of mild solutions. Besides, the source term of an exponential type also causes trouble for us when deriving the desired results. Therefore, powerful embeddings are used to limit the growth of nonlinearity.