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Relevant bibliographies by topics / Fractional Part Inequality

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Academic literature on the topic 'Fractional Part Inequality'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 September 2023

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Journal articles on the topic "Fractional Part Inequality"

1

Song, Hualin, Cheng Hu, and Juan Yu. "Stability and Synchronization of Fractional-Order Complex-Valued Inertial Neural Networks: A Direct Approach." Mathematics 10, no. 24 (2022): 4823. http://dx.doi.org/10.3390/math10244823.

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This paper is dedicated to the asymptotic stability and synchronization for a type of fractional complex-valued inertial neural network by developing a direct analysis method. First, a new fractional differential inequality is presented for nonnegative functions, which provides an effective tool for the convergence analysis of fractional-order systems. Moreover, instead of the previous separation analysis for complex-valued neural networks, a class of Lyapunov functions composed of the complex-valued states and their fractional derivatives is constructed, and some compact stability criteria ar

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2

Hamadneh, Tareq, Amel Hioual, Omar Alsayyed, Yazan Alaya Al-Khassawneh, Abdallah Al-Husban, and Adel Ouannas. "Finite Time Stability Results for Neural Networks Described by Variable-Order Fractional Difference Equations." Fractal and Fractional 7, no. 8 (2023): 616. http://dx.doi.org/10.3390/fractalfract7080616.

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Variable-order fractional discrete calculus is a new and unexplored part of calculus that provides extraordinary capabilities for simulating multidisciplinary processes. Recognizing this incredible potential, the scientific community has been researching variable-order fractional discrete calculus applications to the modeling of engineering and physical systems. This research makes a contribution to the topic by describing and establishing the first generalized discrete fractional variable order Gronwall inequality that we employ to examine the finite time stability of nonlinear Nabla fraction

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3

Tao, Mengfei, and Binlin Zhang. "Solutions for nonhomogeneous fractional (p, q)-Laplacian systems with critical nonlinearities." Advances in Nonlinear Analysis 11, no. 1 (2022): 1332–51. http://dx.doi.org/10.1515/anona-2022-0248.

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Abstract In this article, we aimed to study a class of nonhomogeneous fractional (p, q)-Laplacian systems with critical nonlinearities as well as critical Hardy nonlinearities in R N {{\mathbb{R}}}^{N} . By appealing to a fixed point result and fractional Hardy-Sobolev inequality, the existence of nontrivial nonnegative solutions is obtained. In particular, we also consider Choquard-type nonlinearities in the second part of this article. More precisely, with the help of Hardy-Littlewood-Sobolev inequality, we obtain the existence of nontrivial solutions for the related systems based on the sam

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4

Yuldashev, T. K., and E. T. Karimov. "Mixed type integro-differential equation with fractional order Caputo operators and spectral parameters." Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta 57 (May 2021): 190–205. http://dx.doi.org/10.35634/2226-3594-2021-57-10.

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The issues of unique solvability of a boundary value problem for a mixed type integro-differential equation with two Caputo time-fractional operators and spectral parameters are considered. A mixed type integro-differential equation is a partial integro-differential equation of fractional order in both positive and negative parts of multidimensional rectangular domain under consideration. The fractional Caputo operator's order is less in the positive part of the domain, than the order of Caputo operator in the negative part of the domain. Using the method of Fourier series, two systems of coun

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5

Set, Erhan, Ahmet Akdemir, Emin Özdemir, Ali Karaoğlan, and Mustafa Dokuyucu. "New integral inequalities for Atangana-Baleanu fractional integral operators and various comparisons via simulations." Filomat 37, no. 7 (2023): 2251–67. http://dx.doi.org/10.2298/fil2307251s.

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Integral identities created in inequality theory studies help to prove many inequalities. Recently, different fractional integral and derivative operators have been used to achieve these identities. In this article, with the help of Atangana-Baleanu integral operators, an integral identity was first obtained and various integral inequalities for convex functions have been proved using this identity. In the last part of the article, various simulation graphs are given to reveal the consistency of Atangana-Baleanu fractional integral operators and Riemann-Liouville fractional integral operators

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6

Hansson, Anders M. "On the spectrum and eigenfunctions of the Schrödinger operator with Aharonov-Bohm magnetic field." International Journal of Mathematics and Mathematical Sciences 2005, no. 23 (2005): 3751–66. http://dx.doi.org/10.1155/ijmms.2005.3751.

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We explicitly compute the spectrum and eigenfunctions of the magnetic Schrödinger operatorH(A→,V)=(i∇+A→)2+VinL2(ℝ2), with Aharonov-Bohm vector potential,A→(x1,x2)=α(−x2,x1)/|x|2, and either quadratic or Coulomb scalar potentialV. We also determine sharp constants in the CLR inequality, both dependent on the fractional part ofαand both greater than unity. In the case of quadratic potential, it turns out that the LT inequality holds for allγ≥1with the classical constant, as expected from the nonmagnetic system (harmonic oscillator).

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7

Yuldashev, Tursun K., and Erkinjon T. Karimov. "Inverse Problem for a Mixed Type Integro-Differential Equation with Fractional Order Caputo Operators and Spectral Parameters." Axioms 9, no. 4 (2020): 121. http://dx.doi.org/10.3390/axioms9040121.

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The questions of the one-value solvability of an inverse boundary value problem for a mixed type integro-differential equation with Caputo operators of different fractional orders and spectral parameters are considered. The mixed type integro-differential equation with respect to the main unknown function is an inhomogeneous partial integro-differential equation of fractional order in both positive and negative parts of the multidimensional rectangular domain under consideration. This mixed type of equation, with respect to redefinition functions, is a nonlinear Fredholm type integral equation

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8

Atanacković, Teodor M., Marko Janev, and Stevan Pilipović. "On the thermodynamical restrictions in isothermal deformations of fractional Burgers model." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2172 (2020): 20190278. http://dx.doi.org/10.1098/rsta.2019.0278.

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We investigate, in the distributional setting, the restrictions on the constitutive equation for a fractional Burgers model of viscoelastic fluid that follow from the weak form of the entropy inequality under isothermal conditions. The results are generalized, from the Burgers model, to an arbitrary class of linear constitutive equations with fractional derivatives. Our results show that the restrictions obtained here on the coefficients of constitutive equations are weaker when compared with the restrictions obtained by Bagley–Torvik method. We show the precise relation between restrictions d

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9

Sahoo, Soubhagya Kumar, Muhammad Tariq, Hijaz Ahmad, Jamshed Nasir, Hassen Aydi, and Aiman Mukheimer. "New Ostrowski-Type Fractional Integral Inequalities via Generalized Exponential-Type Convex Functions and Applications." Symmetry 13, no. 8 (2021): 1429. http://dx.doi.org/10.3390/sym13081429.

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Recently, fractional calculus has been the center of attraction for researchers in mathematical sciences because of its basic definitions, properties and applications in tackling real-life problems. The main purpose of this article is to present some fractional integral inequalities of Ostrowski type for a new class of convex mapping. Specifically, n–polynomial exponentially s–convex via fractional operator are established. Additionally, we present a new Hermite–Hadamard fractional integral inequality. Some special cases of the results are discussed as well. Due to the nature of convexity theo

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10

Fahad, Asfand, Ayesha, Yuanheng Wang, and Saad Ihsaan Butt. "Jensen–Mercer and Hermite–Hadamard–Mercer Type Inequalities for GA-h-Convex Functions and Its Subclasses with Applications." Mathematics 11, no. 2 (2023): 278. http://dx.doi.org/10.3390/math11020278.

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Many researchers have been attracted to the study of convex analysis theory due to both facts, theoretical significance, and the applications in optimization, economics, and other fields, which has led to numerous improvements and extensions of the subject over the years. An essential part of the theory of mathematical inequalities is the convex function and its extensions. In the recent past, the study of Jensen–Mercer inequality and Hermite–Hadamard–Mercer type inequalities has remained a topic of interest in mathematical inequalities. In this paper, we study several inequalities for GA-h-co

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Dissertations / Theses on the topic "Fractional Part Inequality"

1

Vivek, Srinivas V. "On A Cubic Sieve Congruence Related To The Discrete Logarithm Problem." Thesis, 2010. https://etd.iisc.ac.in/handle/2005/1996.

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There has been a rapid increase interest in computational number theory ever since the invention of public-key cryptography. Various attempts to solve the underlying hard problems behind public-key cryptosystems has led to interesting problems in computational number theory. One such problem, called the cubic sieve congruence problem, arises in the context of the cubic sieve method for solving the discrete logarithm problem in prime fields. The cubic sieve method requires a nontrivial solution to the Cubic Sieve Congruence (CSC)x3 y2z (mod p), where p is a given prime. A nontrivial solutio

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2

Vivek, Srinivas V. "On A Cubic Sieve Congruence Related To The Discrete Logarithm Problem." Thesis, 2010. http://etd.iisc.ernet.in/handle/2005/1996.

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Abstract:

There has been a rapid increase interest in computational number theory ever since the invention of public-key cryptography. Various attempts to solve the underlying hard problems behind public-key cryptosystems has led to interesting problems in computational number theory. One such problem, called the cubic sieve congruence problem, arises in the context of the cubic sieve method for solving the discrete logarithm problem in prime fields. The cubic sieve method requires a nontrivial solution to the Cubic Sieve Congruence (CSC)x3 y2z (mod p), where p is a given prime. A nontrivial solution

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