Theory and Modern Applications
Page 82 of 98
We investigate second-order half-linear differential equations with asymptotically almost periodic coefficients. For these equations, we explicitly find an oscillation constant. If the coefficients are replace...
In this paper, the generalized q-Bessel function, which is a generalization of the known q-Bessel functions of kinds 1, 2, 3, and the new q-analogy of the modified Bessel function presented in (Mansour and Al-Sho...
In the present study, the first and second order of accuracy stable difference schemes for the numerical solution of the initial boundary value problem for the fractional parabolic equation with the Neumann bo...
In the paper, we consider the existence criteria for positive solutions of the nonlinear p-Laplacian fractional differential equation whose nonlinearity contains the first-order derivative explicitly
In this paper, we investigate some properties of several Sheffer sequences of several polynomials arising from umbral calculus. From our investigation, we can derive many interesting identities of several poly...
In the present paper, we deal with the fractional neutral differential equations involving nonlocal initial conditions. The existence of mild solutions are established. The results are obtained by using the fr...
In this paper, we introduce a unified family of Hermite-based Apostol-Bernoulli, Euler and Genocchi polynomials. We obtain some symmetry identities between these polynomials and the generalized sum of integer ...
The main purpose of this paper is to introduce and investigate a new class of generalized q-Bernoulli and q-Euler polynomials. The q-analogues of well-known formulas are derived. A generalization of the Srivastav...
In this paper, we study the uniqueness of a positive solution for the singular nonlinear fractional differential equation boundary value problem
In this paper, we discuss the existence of weak solutions for a nonlinear boundary value problem of fractional q-difference equations in Banach space. Our analysis relies on the Mönch’s fixed-point theorem combin...
In this article, we establish some new oscillation criteria and give sufficient conditions to ensure that all solutions of nonlinear neutral dynamic equation of the form
This paper presents the following definition, which is a natural combination of the definitions for asymptotically equivalent, ℐ-statistically limit and ℐ-lacunary statistical convergence. Let θ be a lacunary seq...
In the paper, we consider distribution of eigenvalues of a third-order differential operator with nonlocal boundary conditions on a segment. The characteristic operator of the considered spectral problem is an...
In the work, the Cauchy problem is considered for a singularly perturbed system with zero points of the spectrum. It is proved normal solvability of general iterative problems. Unique solvability and convergen...
The main purpose of this paper is to introduce and investigate a class of generalized Bernoulli polynomials and Euler polynomials based on the q-integers. The q-analogues of well-known formulas are derived. The q
In this paper, we introduce the extended 2D Bernoulli polynomials by
We establish the existence and uniqueness of solutions for a class of nonlinear Volterra integral and integro-differential equations using fixed-point theorems for a new variant of cyclic ...
This paper reveals a computational method based using a tau method with Jacobi polynomials for the solution of fuzzy linear fractional differential equations of order
...
In (Kim and Kim in J. Inequal. Appl. 2013:111, 2013; Kim and Kim in Integral Transforms Spec. Funct., 2013, doi:10.1080/10652469.2012.754756), we have investigated some properties of higher-order Bernoulli and...
In this paper, we discuss numerical methods for fractional order problems. Some nonstandard finite difference schemes are presented and investigated. The application in the simulation of a fractional-order Bru...
The purpose of the present paper is to investigate various mapping and inclusion properties involving subclasses of analytic and univalent functions for a linear operator defined by means of Hadamard product (...
The universal real constant pi, the ratio of the circumference of any circle and its diameter, has no exact numerical representation in a finite number of digits in any number/radix system. It has conjured up ...
In this paper, we rigorously prove the existence of chaos in a class of delay difference equations, which can be viewed as a discrete analogue of a one-dimensional delay differential equation by using the Eule...
In this paper, we investigate the value distribution of difference polynomial and obtain the following result, which improves a recent result of K. Liu and L.Z. Yang: Let f be a transcendental meromorphic functio...
This paper points out the fractional complex transform method for wave equations on Cantor sets within the local differential fractional operators. The proposed method is efficient to handle differential equat...
The fundamental aim of this paper is to consider some applications of umbral calculus by utilizing from the extended p-adic q-invariant integral on
In this paper, we study the equilibrium points, local asymptotic stability of equilibrium points, and global behavior of equilibrium points of a discrete Lotka-Volterra model given by
In this paper, we make use of the relatively new analytical technique, the homotopy decomposition method (HDM), to solve a system of fractional nonlinear differential equations that arise in the model for HIV ...
The purpose of the present paper is to investigate some subordination- and superordination-preserving properties of certain nonlinear integral operators defined on the space of meromorphically p-valent functions ...
Asymptotic properties of solutions of a difference equation of the form
The purpose of this paper is to investigate a nonlinear second-order neutral difference equation of the form
In this paper, we study the zeros of difference polynomials of meromorphic functions of the forms
The main object of the present paper is to show certain sufficient conditions for univalency of analytic functions with missing coefficients.
By using Mawhin’s continuation theorem in the coincidence degree theory, some criteria for guaranteeing the existence of periodic solutions for prescribed mean curvature Rayleigh equation with a deviating argu...
A discrete SIS epidemic model with stage structure and standard incident rate which is governed by Beverton-Holt type is studied. The sufficient conditions on the permanence and extinction of disease are estab...
We investigate symplectic difference systems with periodic coefficients. We show that the known traffic rules for eigenvalues of the monodromy matrix of linear Hamiltonian differential and difference systems c...
In this paper, by using a fixed point result on ordered metric spaces, we prove the existence and uniqueness of a solution of the nonlinear fractional differential equation ...
In this paper we consider the second-order linear difference equations with variable delays
In the present paper, we introduce two-parameter Srivastava polynomials in one, two and three variables by inserting new indices, where in the special cases they reduce to (among others) Laguerre, Jacobi, Bess...
The space fractional Schrödinger equation was further extended to the concept of space fractional variable-order derivative. The generalized equation is very difficult to handle analytically. We solved the gen...
Host parasite models are similar to host parasitoid models except that the parasite does not necessarily kill the host. Leslie/Gower model (Leslie and Gower in Biometrika 47(3/4):219-234, 1960) played a histor...
We study a new class of boundary value problems of nonlinear fractional differential equations whose nonlinear term depends on a lower-order fractional derivative with fractional separated boundary conditions....
The space of Boehmians is constructed using an algebraic approach that utilizes convolution and approximate identities or delta sequences. A proper subspace can be identified with the space of distributions. I...
In this paper, we will establish a theory for the power series method that can be applied to various types of linear differential equations of second order to prove the Hyers-Ulam stability.
In view of the Nevanlinna theory, we study the growth and poles of solutions of some classes of systems of complex difference equations and obtain some interesting results such as the lower bounds for Nevanlin...
Using p-adic integral, many new convolution identities involving Bernoulli, Euler and Genocchi numbers are given.
In this paper, we derive the identities of higher-order Bernoulli, Euler and Frobenius-Euler polynomials from the orthogonality of Hermite polynomials. Finally, we give some interesting and new identities of s...
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