International Journal of Differential Equations

https://www.hindawi.com/journals/ijde/

List of Papers (Total 577)

Some Comparison of Solutions by Different Numerical Techniques on Mathematical Biology Problem

We try to compare the solutions by some numerical techniques when we apply the methods on some mathematical biology problems. The Runge-Kutta-Fehlberg (RKF) method is a promising method to give an approximate solution of nonlinear ordinary differential equation systems, such as a model for insect population, one-species Lotka-Volterra model. The technique is described and...

Some Comparison of Solutions by Different Numerical Techniques on Mathematical Biology Problem

We try to compare the solutions by some numerical techniques when we apply the methods on some mathematical biology problems. The Runge-Kutta-Fehlberg (RKF) method is a promising method to give an approximate solution of nonlinear ordinary differential equation systems, such as a model for insect population, one-species Lotka-Volterra model. The technique is described and...

Existence of Solutions for Fractional Impulsive Integrodifferential Equations in Banach Spaces

We investigate the existence of solutions for a class of impulsive fractional evolution equations with nonlocal conditions in Banach space by using some fixed point theorems combined with the technique of measure of noncompactness. Our results improve and generalize some known results corresponding to those obtained by others. Finally, two applications are given to illustrate...

Existence of Solutions for Fractional Impulsive Integrodifferential Equations in Banach Spaces

We investigate the existence of solutions for a class of impulsive fractional evolution equations with nonlocal conditions in Banach space by using some fixed point theorems combined with the technique of measure of noncompactness. Our results improve and generalize some known results corresponding to those obtained by others. Finally, two applications are given to illustrate...

The Dynamical Analysis of a Prey-Predator Model with a Refuge-Stage Structure Prey Population

We proposed and analyzed a mathematical model dealing with two species of prey-predator system. It is assumed that the prey is a stage structure population consisting of two compartments known as immature prey and mature prey. It has a refuge capability as a defensive property against the predation. The existence, uniqueness, and boundedness of the solution of the proposed model...

About a Problem for Loaded Parabolic-Hyperbolic Type Equation with Fractional Derivatives

An existence and uniqueness of solution of local boundary value problem with discontinuous matching condition for the loaded parabolic-hyperbolic equation involving the Caputo fractional derivative and Riemann-Liouville integrals have been investigated. The uniqueness of solution is proved by the method of integral energy and the existence is proved by the method of integral...

About a Problem for Loaded Parabolic-Hyperbolic Type Equation with Fractional Derivatives

An existence and uniqueness of solution of local boundary value problem with discontinuous matching condition for the loaded parabolic-hyperbolic equation involving the Caputo fractional derivative and Riemann-Liouville integrals have been investigated. The uniqueness of solution is proved by the method of integral energy and the existence is proved by the method of integral...

Piecewise Approximate Analytical Solutions of High-Order Singular Perturbation Problems with a Discontinuous Source Term

A reliable algorithm is presented to develop piecewise approximate analytical solutions of third- and fourth-order convection diffusion singular perturbation problems with a discontinuous source term. The algorithm is based on an asymptotic expansion approximation and Differential Transform Method (DTM). First, the original problem is transformed into a weakly coupled system of...

Positive Solutions to Periodic Boundary Value Problems of Nonlinear Fractional Differential Equations at Resonance

By Leggett-Williams norm-type theorem for coincidences due to O’Regan and Zima, we discuss the existence of positive solutions to fractional order with periodic boundary conditions at resonance. At last, an example is presented to demonstrate the main results.

Multiplicity Results for the -Laplacian Equation with Singular Nonlinearities and Nonlinear Neumann Boundary Condition

We investigate the singular Neumann problem involving the -Laplace operator:   , in  , where is a bounded domain with boundary, is a positive parameter, and , and are assumed to satisfy assumptions (H0)–(H5) in the Introduction. Using some variational techniques, we show the existence of a number such that problem has two solutions for one solution for , and no solutions for .

Multiplicity Results for the -Laplacian Equation with Singular Nonlinearities and Nonlinear Neumann Boundary Condition

We investigate the singular Neumann problem involving the -Laplace operator:   , in  , where is a bounded domain with boundary, is a positive parameter, and , and are assumed to satisfy assumptions (H0)–(H5) in the Introduction. Using some variational techniques, we show the existence of a number such that problem has two solutions for one solution for , and no solutions for .

Multiplicity Results for the -Laplacian Equation with Singular Nonlinearities and Nonlinear Neumann Boundary Condition

We investigate the singular Neumann problem involving the -Laplace operator:   , in  , where is a bounded domain with boundary, is a positive parameter, and , and are assumed to satisfy assumptions (H0)–(H5) in the Introduction. Using some variational techniques, we show the existence of a number such that problem has two solutions for one solution for , and no solutions for .

Error Analysis of an Implicit Spectral Scheme Applied to the Schrödinger-Benjamin-Ono System

We develop error estimates of the semidiscrete and fully discrete formulations of a Fourier-Galerkin numerical scheme to approximate solutions of a coupled nonlinear Schrödinger-Benjamin-Ono system that describes the motion of two fluids with different densities under capillary-gravity waves in a deep water regime. The accuracy of the numerical solver is checked using some exact...

Dirichlet Boundary Value Problem for the Second Order Asymptotically Linear System

We consider the second order system with the Dirichlet boundary conditions , where the vector field is asymptotically linear and . We provide the existence and multiplicity results using the vector field rotation theory.

Error Analysis of an Implicit Spectral Scheme Applied to the Schrödinger-Benjamin-Ono System

We develop error estimates of the semidiscrete and fully discrete formulations of a Fourier-Galerkin numerical scheme to approximate solutions of a coupled nonlinear Schrödinger-Benjamin-Ono system that describes the motion of two fluids with different densities under capillary-gravity waves in a deep water regime. The accuracy of the numerical solver is checked using some exact...

Dirichlet Boundary Value Problem for the Second Order Asymptotically Linear System

We consider the second order system with the Dirichlet boundary conditions , where the vector field is asymptotically linear and . We provide the existence and multiplicity results using the vector field rotation theory.

A Numerical Computation of a System of Linear and Nonlinear Time Dependent Partial Differential Equations Using Reduced Differential Transform Method

This paper deals with an analytical solution of an initial value system of time dependent linear and nonlinear partial differential equations by implementing reduced differential transform (RDT) method. The effectiveness and the convergence of RDT method are tested by means of five test problems, which indicates the validity and great potential of the reduced differential...

A Numerical Computation of a System of Linear and Nonlinear Time Dependent Partial Differential Equations Using Reduced Differential Transform Method

This paper deals with an analytical solution of an initial value system of time dependent linear and nonlinear partial differential equations by implementing reduced differential transform (RDT) method. The effectiveness and the convergence of RDT method are tested by means of five test problems, which indicates the validity and great potential of the reduced differential...

Multiple Solutions for the Asymptotically Linear Kirchhoff Type Equations on

The multiplicity of positive solutions for Kirchhoff type equations depending on a nonnegative parameter on is proved by using variational method. We will show that if the nonlinearities are asymptotically linear at infinity and is sufficiently small, the Kirchhoff type equations have at least two positive solutions. For the perturbed problem, we give the result of existence of...

On Accuracy and Stability Analysis of the Reproducing Kernel Space Method for the Forced Duffing Equation

It is attempted to provide the stability and convergence analysis of the reproducing kernel space method for solving the Duffing equation with with boundary integral conditions. We will prove that the reproducing space method is stable. Moreover, after introducing the method, it is shown that it has convergence order two.

The Maximal Strichartz Family of Gaussian Distributions: Fisher Information, Index of Dispersion, and Stochastic Ordering

We define and study several properties of what we call Maximal Strichartz Family of Gaussian Distributions. This is a subfamily of the family of Gaussian Distributions that arises naturally in the context of the Linear Schrödinger Equation and Harmonic Analysis, as the set of maximizers of certain norms introduced by Strichartz. From a statistical perspective, this family carries...

A Hybrid Natural Transform Homotopy Perturbation Method for Solving Fractional Partial Differential Equations

A hybrid analytical method for solving linear and nonlinear fractional partial differential equations is presented. The proposed analytical approach is an elegant combination of the Natural Transform Method (NTM) and a well-known method, Homotopy Perturbation Method (HPM). In this analytical method, the fractional derivative is computed in Caputo sense and the nonlinear term is...

A Hybrid Natural Transform Homotopy Perturbation Method for Solving Fractional Partial Differential Equations

A hybrid analytical method for solving linear and nonlinear fractional partial differential equations is presented. The proposed analytical approach is an elegant combination of the Natural Transform Method (NTM) and a well-known method, Homotopy Perturbation Method (HPM). In this analytical method, the fractional derivative is computed in Caputo sense and the nonlinear term is...

Symmetry Classification and Exact Solutions of a Variable Coefficient Space-Time Fractional Potential Burgers’ Equation

We investigate the symmetry properties of a variable coefficient space-time fractional potential Burgers’ equation. Fractional Lie symmetries and corresponding infinitesimal generators are obtained. With the help of the infinitesimal generators, some group invariant solutions are deduced. Further, some exact solutions of fractional potential Burgers’ equation are generated by the...

Symmetry Classification and Exact Solutions of a Variable Coefficient Space-Time Fractional Potential Burgers’ Equation

We investigate the symmetry properties of a variable coefficient space-time fractional potential Burgers’ equation. Fractional Lie symmetries and corresponding infinitesimal generators are obtained. With the help of the infinitesimal generators, some group invariant solutions are deduced. Further, some exact solutions of fractional potential Burgers’ equation are generated by the...