Theory and Modern Applications
Page 5 of 98
In this paper, for the first time the inverse problem of reconstructing the time-dependent potential (TDP) and displacement distribution in the hyperbolic problem with periodic boundary conditions (BCs) and no...
Infection of hepatitis B virus (HBV) is a global health problem. We provide the study about hepatitis B virus dynamics that can be controlled by education campaign (awareness), vaccination, and treatment. Init...
Some complicated events can be modeled by systems of differential equations. On the other hand, inclusion systems can describe complex phenomena having some shocks better than the system of differential equati...
The aim of this paper is to investigate the interpolative contractions involving rational forms in the framework of b-metric spaces. We prove the existence of a fixed point of such a mapping with different combin...
In the work (Bouaouid et al. in Adv. Differ. Equ. 2019:21, 2019), the authors have used the Krasnoselskii fixed point theorem for showing the existence of mild solutions of an abstract class of conformable fracti...
In this work, we consider a quasilinear system of viscoelastic equations with degenerate damping and general source terms. According to some suitable hypothesis, we study the blow-up of solutions. This is the ...
The main target of this paper is to study a problem of recovering a spherically symmetric domain with fractional derivative from observed data of nonlocal type. This problem can be established as a new boundar...
A memristor is naturally a nonlinear and at the same time memory element that may substitute resistors for next-generation nonlinear computational circuits that can show complex behaviors including chaos. A fo...
The interaction among phytoplankton and zooplankton is one of the most important processes in ecology. Discrete-time mathematical models are commonly used for describing the dynamical properties of phytoplankt...
The Correction to this article has been published in Advances in Difference Equations 2021 2021:519
In this paper, we present a new structure of the n-dimensional trigonometric cubic B-spline collocation algorithm, which we show in three different formats: one-, two-, and three-dimensional. These constructs are...
This paper deals with Al-Salam fractional q-integral operator and its application to certain q-analogues of Bessel functions and power series. Al-Salam fractional q-integral operator has been applied to various t...
In the present investigation, with the help of certain higher-order q-derivatives, some new subclasses of multivalent q-starlike functions which are associated with the Janowski functions are defined. Then, certa...
This paper proposes two numerical approaches for solving the coupled nonlinear time-fractional Burgers’ equations with initial or boundary conditions on the interval
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A three-species non-autonomous stochastic Lotka–Volterra food web system in a polluted environment is proposed, and the existence of positive periodic solutions of this system is established by constructing a ...
In this work, we establish some necessary results about existence theory to a class of boundary value problems (BVPs) of hybrid fractional differential equations (HFDEs) in the frame of Atangana–Baleanu–Caputo (A...
In this research, we study a general class of variable order integro-differential equations (VO-IDEs). We propose a numerical scheme based on the shifted fifth-kind Chebyshev polynomials (SFKCPs). First, in th...
In this paper, we consider the biparabolic problem under nonlocal conditions with both linear and nonlinear source terms. We derive the regularity property of the mild solution for the linear source term while...
In this paper, we consider a fractional-order model of a brushless DC motor. To develop a mathematical model, we use the concept of the Liouville–Caputo noninteger derivative with the Mittag-Lefler kernel. We ...
In this paper, we investigate the growth and fixed points of solutions of higher-order linear differential equations in the unit disc. We extend the coefficient conditions to a type of one-constant-control coe...
By introducing some parameters perturbed by white noises, we propose a class of stochastic inertial neural networks in random environments. Constructing two Lyapunov–Krasovskii functionals, we establish the me...
HIV patients are vulnerable to developing active visceral leishmaniasis (VL). To understand this complication, we studied a mathematical model for HIV and visceral leishmaniasis coinfection. In this approach, ...
In this paper, we consider a new coupled system of fractional boundary value problems based on the thermostat control model. With the help of fixed point theory, we investigate the existence criterion of the s...
Various attempts have been made in defining the derivative of a quaternionic function due to the noncommutativity of the product over quaternions. We observe that the difference in the left and right operation...
In this paper, we present a numerical technique for solving fractional optimal control problems with a fractional derivative called Caputo–Katugampola derivative. This derivative is a generalization of the Cap...
The main objective of this paper is to investigate the existence, uniqueness, and Ulam–Hyers stability of positive solutions for fractional integro-differential boundary values problem. Uniqueness result is ob...
The original article was published in Advances in Difference Equations 2021 2021:183
The aim of this paper is to introduce the degenerate generalized Laguerre polynomials as the degenerate version of the generalized Laguerre polynomials and to derive some properties related to those polynomial...
Recently, Kim et al. (Adv. Differ. Equ. 2020:168, 2020) considered the poly-Bernoulli numbers and polynomials resulting from the moderated version of degenerate polyexponential functions. In this paper, we invest...
In this research paper, we improve some fractional integral inequalities of Minkowski-type. Precisely, we use a proportional fractional integral operator with respect to another strictly increasing continuous ...
Motivated by the recent studies and developments of the integral transforms with various special matrix functions, including the matrix orthogonal polynomials as kernels, in this article we derive the formulas...
The main purpose of this paper is to present some fixed-point results for a pair of fuzzy dominated mappings which are generalized V-contractions in modular-like metric spaces. Some theorems using a partial order...
In this article, we consider a temporally second-order unconditionally energy stable computational method for the Allen–Cahn (AC) equation with a high-order polynomial free energy potential. By modifying the n...
The local dynamics with different topological classifications, bifurcation analysis, and chaos control for the phytoplankton–zooplankton model, which is a discrete analogue of the continuous-time model by a fo...
In this work, we solve the system of integro-differential equations (in terms of Caputo–Fabrizio calculus) using the concepts of the best proximity pair (point) and measure of noncompactness. We first introduc...
The aim of this study is to introduce a new interpolative contractive mapping combining the Hardy–Rogers contractive mapping of Suzuki type and
In this work, we aim at studying the asymptotic and oscillatory behavior of even-order neutral delay noncanonical differential equations. To the best of our knowledge, most of the related previous works are co...
In this paper, we introduce multi-Lah numbers and multi-Stirling numbers of the first kind and recall multi-Bernoulli numbers, all of whose generating functions are given with the help of multiple logarithm. T...
In this work, we modify the inertial hybrid algorithm with Armijo line search using a parallel method to approximate a common solution of nonmonotone equilibrium problems in Hilbert spaces. A weak convergence ...
In this paper, we propose two new contractions via simulation function that involves rational expression in the setting of partial b-metric space. The obtained results not only extend, but also generalize and ...
A number of mathematical methods have been developed to determine the complex rheological behavior of fluid’s models. Such mathematical models are investigated using statistical, empirical, analytical, and ite...
A remarkably large number of hypergeometric (and generalized) functions and a variety of their extensions have been presented and investigated in the literature by many authors. In this paper, we introduce fiv...
In this paper, we consider the existence of multiple periodic solutions for a class of second-order difference equations with quadratic–supquadratic growth condition at infinity. Moreover, we give three exampl...
Cholera is a waterborne disease that continues to pose serious public health problems in many developing countries. Increasing water and sanitation coverage is a goal for local authorities in these countries, ...
In this paper, we study the existence of solutions for a generalized sequential Caputo-type fractional neutral differential inclusion with generalized integral conditions. The used fractional operator has the ...
Fractional calculus as was predicted by Leibniz to be a paradox, has nowadays evolved to become a centre of interest for many researchers from various backgrounds. As a result, multiple innovative ideas had em...
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