Let X be a complex Banach space and let B and C be two closed linear operators on X satisfying the condition D(B)?D(C),and let d∈L^(1)(R_(+))and 0≤β<α≤2.We characterize the well-posedness of the fractional int...Let X be a complex Banach space and let B and C be two closed linear operators on X satisfying the condition D(B)?D(C),and let d∈L^(1)(R_(+))and 0≤β<α≤2.We characterize the well-posedness of the fractional integro-differential equations D^(α)u(t)+CD^(β)u(t)=Bu(t)+∫_(-∞)td(t-s)Bu(s)ds+f(t),(0≤t≤2π)on periodic Lebesgue-Bochner spaces L^(p)(T;X)and periodic Besov spaces B_(p,q)^(s)(T;X).展开更多
This paper investigates the maximal and minimal solutions of initial value problems for second order nonlinear integro-differential equations of Volterra type on a finite interval in a Banach space by establishing a c...This paper investigates the maximal and minimal solutions of initial value problems for second order nonlinear integro-differential equations of Volterra type on a finite interval in a Banach space by establishing a comparison result and using the monotone iterative technique.展开更多
In this paper, using Sadovskii’s fixed point theorem and properties of the measure of noncompactness, we obtain asymptotic stability results for solutions of nonlinear differential equation with variable delay. Resul...In this paper, using Sadovskii’s fixed point theorem and properties of the measure of noncompactness, we obtain asymptotic stability results for solutions of nonlinear differential equation with variable delay. Results presented in this paper extend some previous results due to Burton?[1], Becker and Burton?[2], Ardjouni and Djoudi [3], and Jin and Luo?[4].展开更多
In this paper, the author obtains an existence theorem of minimal and maximal solutions for the periodic boundary value problems of nonlinear impulsive integrodifferential equations of mixed type in Banach space by me...In this paper, the author obtains an existence theorem of minimal and maximal solutions for the periodic boundary value problems of nonlinear impulsive integrodifferential equations of mixed type in Banach space by means of the monotone iterative technique and cone theory based on a comparison result.展开更多
The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators Lp-multipliers and UMD-s...The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators Lp-multipliers and UMD-spaces.展开更多
In this paper,we present the existence and uniqueness of fixed points and common fixed points for Reich and Chatterjea pairs of self-maps in complete metric spaces.Furthermore,we study fixed point theorems for Reich a...In this paper,we present the existence and uniqueness of fixed points and common fixed points for Reich and Chatterjea pairs of self-maps in complete metric spaces.Furthermore,we study fixed point theorems for Reich and Chatterjea nonexpansive mappings in a Banach space using the Krasnoselskii-Ishikawa iteration method associated withSλand consider some applications of our results to prove the existence of solutions for nonlinear integral and nonlinear fractional differential equations.We also establish certain interesting examples to illustrate the usability of our results.展开更多
This paper describes an approximating solution, based on Lagrange interpolation and spline functions, to treat functional integral equations of Fredholm type and Volterra type. This method extended to functional integ...This paper describes an approximating solution, based on Lagrange interpolation and spline functions, to treat functional integral equations of Fredholm type and Volterra type. This method extended to functional integral and integro-differential equations. For showing efficiency of the method we give some numerical examples.展开更多
In this paper, we apply the differential transformation method to high-order nonlinear Volterra- Fredholm integro-differential equations with se- parable kernels. Some different examples are considered the results of ...In this paper, we apply the differential transformation method to high-order nonlinear Volterra- Fredholm integro-differential equations with se- parable kernels. Some different examples are considered the results of these examples indi-cated that the procedure of the differential transformation method is simple and effective, and could provide an accurate approximate solution or exact solution.展开更多
In this paper we study the higher-order differential variational principle and differential equations of motion for mechanical systems in event space. Based on the higher-order d'Alembert principle of the system, the...In this paper we study the higher-order differential variational principle and differential equations of motion for mechanical systems in event space. Based on the higher-order d'Alembert principle of the system, the higher-order velocity energy and the higher-order acceleration energy of the system in event space are defined, the higher-order d'Alembert- Lagrange principle of the system in event space is established, and the parametric forms of Euler-Lagrange, Nielsen and Appell for this principle are given. Finally, the higher-order differential equations of motion for holonomic systems in event space are obtained.展开更多
In this article,a new algorithm is presented to solve the nonlinear impulsive differential equations.In the first time,this article combines the reproducing kernel method with the least squares method to solve the sec...In this article,a new algorithm is presented to solve the nonlinear impulsive differential equations.In the first time,this article combines the reproducing kernel method with the least squares method to solve the second-order nonlinear impulsive differential equations.Then,the uniform convergence of the numerical solution is proved,and the time consuming Schmidt orthogonalization process is avoided.The algorithm is employed successfully on some numerical examples.展开更多
The aim of this work is to study the existence of periodic solutions of integro-differential equations , (0 ≤ t ≤ 2π) with the periodic condition x(0) = x(2π) , where a ∈ L<sup>1</sup> (R<sub>+&...The aim of this work is to study the existence of periodic solutions of integro-differential equations , (0 ≤ t ≤ 2π) with the periodic condition x(0) = x(2π) , where a ∈ L<sup>1</sup> (R<sub>+</sub>). Our approach is based on the M-boundedness of linear operators B<sup>s</sup><sub>p,q</sub>-multipliers and some results in Besov space.展开更多
This paper investigates periodic boundary value problem for first order nonlinear impulsive integro-differelltial equations of mixed type in a Banach space. By establishing a comparison result, criteria on the existen...This paper investigates periodic boundary value problem for first order nonlinear impulsive integro-differelltial equations of mixed type in a Banach space. By establishing a comparison result, criteria on the existence of maximal and minimal solutions are obtained.展开更多
We introduce a novel numerical method for solving two-sided space fractional partial differential equations in two-dimensional case.The approximation of the space fractional Riemann-Liouville derivative is based on th...We introduce a novel numerical method for solving two-sided space fractional partial differential equations in two-dimensional case.The approximation of the space fractional Riemann-Liouville derivative is based on the approximation of the Hadamard finite-part integral which has the convergence order O(h^3-a),where h is the space step size and α∈(1,2)is the order of Riemann-Liouville fractional derivative.Based on this scheme,we introduce a shifted finite difference method for solving space fractional partial differential equations.We obtained the error estimates with the convergence orders O(τ+h^3-a+h^β),where τ is the time step size and β>0 is a parameter which measures the smoothness of the fractional derivatives of the solution of the equation.Unlike the numerical methods for solving space fractional partial differential equations constructed using the standard shifted Griinwald-Letnikov formula or higher order Lubich's methods which require the solution of the equation to satisfy the homogeneous Dirichlet boundary condition to get the firstorder convergence,the numerical method for solving the space fractional partial differential equation constructed using the Hadamard finite-part integral approach does not require the solution of the equation to satisfy the Dirichlet homogeneous boundary condition.Numerical results show that the experimentally determined convergence order obtained using the Hadamard finite-part integral approach for solving the space fractional partial differential equation with non-homogeneous Dirichlet boundary conditions is indeed higher than the convergence order obtained using the numerical methods constructed with the standard shifted Griinwald-Letnikov formula or Lubich's higher order approximation schemes.展开更多
The modelling of risky asset by stochastic processes with continuous paths, based on Brow- nian motions, suffers from several defects. First, the path continuity assumption does not seem reason- able in view of the po...The modelling of risky asset by stochastic processes with continuous paths, based on Brow- nian motions, suffers from several defects. First, the path continuity assumption does not seem reason- able in view of the possibility of sudden price variations (jumps) resulting of market crashes. A solution is to use stochastic processes with jumps, that will account for sudden variations of the asset prices. On the other hand, such jump models are generally based on the Poisson random measure. Many popular economic and financial models described by stochastic differential equations with Poisson jumps. This paper deals with the approximate controllability of a class of second-order neutral stochastic differential equations with infinite delay and Poisson jumps. By using the cosine family of operators, stochastic analysis techniques, a new set of sufficient conditions are derived for the approximate controllability of the above control system. An example is provided to illustrate the obtained theory.展开更多
By means of the method of coupled lower and upper quasisolutio ns, the paper applies, instead of establishing the comparison theorem, a new ite rative technique to nonlinear impulsive Fredholm integral equations in ...By means of the method of coupled lower and upper quasisolutio ns, the paper applies, instead of establishing the comparison theorem, a new ite rative technique to nonlinear impulsive Fredholm integral equations in Banach sp aces and proves the existence theorem on their coupled extremal quasisolutions . Finally, an infinite system of nonlinear impulsive integral equations is provi ded to demonstrate the obtained results.展开更多
We study a nonlinear differential equations in the Banach space of real functions and continuous on a bounded and closed interval. With the help of a suitable theorems (fixed point) and some boundary conditions, the 5...We study a nonlinear differential equations in the Banach space of real functions and continuous on a bounded and closed interval. With the help of a suitable theorems (fixed point) and some boundary conditions, the 5th order nonlinear differential equations has at least one positive solution.展开更多
In this paper, a Darbao type random fixed point theorem for a system of weak continuous random operators with random domain is first proved. When, by using the theorem, some existence criteria of random solutions for ...In this paper, a Darbao type random fixed point theorem for a system of weak continuous random operators with random domain is first proved. When, by using the theorem, some existence criteria of random solutions for a systems of nonlinear random Volterra integral equations relative to the weak topology in Banach spaces are given. As applications, some existence theorems of weak random solutions for the random Cauchy problem of a system of nonlinear random differential equations are obtained, as well as the existence of extremal random solutions and random comparison results for these systems of random equations relative to weak topology in Banach spaces. The corresponding results of Szep, Mitchell-Smith, Cramer-Lakshmikantham, Lakshmikantham-Leela and Ding are improved and generalized by these theorems.展开更多
基金the NSF of China(12171266,12171062)the NSF of Chongqing(CSTB2022NSCQ-JQX0004)。
文摘Let X be a complex Banach space and let B and C be two closed linear operators on X satisfying the condition D(B)?D(C),and let d∈L^(1)(R_(+))and 0≤β<α≤2.We characterize the well-posedness of the fractional integro-differential equations D^(α)u(t)+CD^(β)u(t)=Bu(t)+∫_(-∞)td(t-s)Bu(s)ds+f(t),(0≤t≤2π)on periodic Lebesgue-Bochner spaces L^(p)(T;X)and periodic Besov spaces B_(p,q)^(s)(T;X).
文摘This paper investigates the maximal and minimal solutions of initial value problems for second order nonlinear integro-differential equations of Volterra type on a finite interval in a Banach space by establishing a comparison result and using the monotone iterative technique.
文摘In this paper, using Sadovskii’s fixed point theorem and properties of the measure of noncompactness, we obtain asymptotic stability results for solutions of nonlinear differential equation with variable delay. Results presented in this paper extend some previous results due to Burton?[1], Becker and Burton?[2], Ardjouni and Djoudi [3], and Jin and Luo?[4].
文摘In this paper, the author obtains an existence theorem of minimal and maximal solutions for the periodic boundary value problems of nonlinear impulsive integrodifferential equations of mixed type in Banach space by means of the monotone iterative technique and cone theory based on a comparison result.
文摘The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators Lp-multipliers and UMD-spaces.
文摘In this paper,we present the existence and uniqueness of fixed points and common fixed points for Reich and Chatterjea pairs of self-maps in complete metric spaces.Furthermore,we study fixed point theorems for Reich and Chatterjea nonexpansive mappings in a Banach space using the Krasnoselskii-Ishikawa iteration method associated withSλand consider some applications of our results to prove the existence of solutions for nonlinear integral and nonlinear fractional differential equations.We also establish certain interesting examples to illustrate the usability of our results.
文摘This paper describes an approximating solution, based on Lagrange interpolation and spline functions, to treat functional integral equations of Fredholm type and Volterra type. This method extended to functional integral and integro-differential equations. For showing efficiency of the method we give some numerical examples.
文摘In this paper, we apply the differential transformation method to high-order nonlinear Volterra- Fredholm integro-differential equations with se- parable kernels. Some different examples are considered the results of these examples indi-cated that the procedure of the differential transformation method is simple and effective, and could provide an accurate approximate solution or exact solution.
基金Project supported by the Science and Technology Program of Xi’an City,China(Grant No.CXY1352WL34)
文摘In this paper we study the higher-order differential variational principle and differential equations of motion for mechanical systems in event space. Based on the higher-order d'Alembert principle of the system, the higher-order velocity energy and the higher-order acceleration energy of the system in event space are defined, the higher-order d'Alembert- Lagrange principle of the system in event space is established, and the parametric forms of Euler-Lagrange, Nielsen and Appell for this principle are given. Finally, the higher-order differential equations of motion for holonomic systems in event space are obtained.
基金This work is supported by a Young Innovative Talents Program in Universities and Colleges of Guangdong Province(2018KQNCX338)two Scientific Research-Innovation Team Projects at Zhuhai Campus,Beijing Institute of Technology(XK-2018-15,XK-2019-10).
文摘In this article,a new algorithm is presented to solve the nonlinear impulsive differential equations.In the first time,this article combines the reproducing kernel method with the least squares method to solve the second-order nonlinear impulsive differential equations.Then,the uniform convergence of the numerical solution is proved,and the time consuming Schmidt orthogonalization process is avoided.The algorithm is employed successfully on some numerical examples.
文摘The aim of this work is to study the existence of periodic solutions of integro-differential equations , (0 ≤ t ≤ 2π) with the periodic condition x(0) = x(2π) , where a ∈ L<sup>1</sup> (R<sub>+</sub>). Our approach is based on the M-boundedness of linear operators B<sup>s</sup><sub>p,q</sub>-multipliers and some results in Besov space.
文摘This paper investigates periodic boundary value problem for first order nonlinear impulsive integro-differelltial equations of mixed type in a Banach space. By establishing a comparison result, criteria on the existence of maximal and minimal solutions are obtained.
基金Y.Wang's research was supported by the Natural Science Foundation of Luliang University(XN201510).
文摘We introduce a novel numerical method for solving two-sided space fractional partial differential equations in two-dimensional case.The approximation of the space fractional Riemann-Liouville derivative is based on the approximation of the Hadamard finite-part integral which has the convergence order O(h^3-a),where h is the space step size and α∈(1,2)is the order of Riemann-Liouville fractional derivative.Based on this scheme,we introduce a shifted finite difference method for solving space fractional partial differential equations.We obtained the error estimates with the convergence orders O(τ+h^3-a+h^β),where τ is the time step size and β>0 is a parameter which measures the smoothness of the fractional derivatives of the solution of the equation.Unlike the numerical methods for solving space fractional partial differential equations constructed using the standard shifted Griinwald-Letnikov formula or higher order Lubich's methods which require the solution of the equation to satisfy the homogeneous Dirichlet boundary condition to get the firstorder convergence,the numerical method for solving the space fractional partial differential equation constructed using the Hadamard finite-part integral approach does not require the solution of the equation to satisfy the Dirichlet homogeneous boundary condition.Numerical results show that the experimentally determined convergence order obtained using the Hadamard finite-part integral approach for solving the space fractional partial differential equation with non-homogeneous Dirichlet boundary conditions is indeed higher than the convergence order obtained using the numerical methods constructed with the standard shifted Griinwald-Letnikov formula or Lubich's higher order approximation schemes.
基金supported by the National Board for Higher Mathematics,Mumbai,India under Grant No.2/48(5)/2013/NBHM(R.P.)/RD-II/688 dt 16.01.2014
文摘The modelling of risky asset by stochastic processes with continuous paths, based on Brow- nian motions, suffers from several defects. First, the path continuity assumption does not seem reason- able in view of the possibility of sudden price variations (jumps) resulting of market crashes. A solution is to use stochastic processes with jumps, that will account for sudden variations of the asset prices. On the other hand, such jump models are generally based on the Poisson random measure. Many popular economic and financial models described by stochastic differential equations with Poisson jumps. This paper deals with the approximate controllability of a class of second-order neutral stochastic differential equations with infinite delay and Poisson jumps. By using the cosine family of operators, stochastic analysis techniques, a new set of sufficient conditions are derived for the approximate controllability of the above control system. An example is provided to illustrate the obtained theory.
文摘By means of the method of coupled lower and upper quasisolutio ns, the paper applies, instead of establishing the comparison theorem, a new ite rative technique to nonlinear impulsive Fredholm integral equations in Banach sp aces and proves the existence theorem on their coupled extremal quasisolutions . Finally, an infinite system of nonlinear impulsive integral equations is provi ded to demonstrate the obtained results.
文摘We study a nonlinear differential equations in the Banach space of real functions and continuous on a bounded and closed interval. With the help of a suitable theorems (fixed point) and some boundary conditions, the 5th order nonlinear differential equations has at least one positive solution.
文摘In this paper, a Darbao type random fixed point theorem for a system of weak continuous random operators with random domain is first proved. When, by using the theorem, some existence criteria of random solutions for a systems of nonlinear random Volterra integral equations relative to the weak topology in Banach spaces are given. As applications, some existence theorems of weak random solutions for the random Cauchy problem of a system of nonlinear random differential equations are obtained, as well as the existence of extremal random solutions and random comparison results for these systems of random equations relative to weak topology in Banach spaces. The corresponding results of Szep, Mitchell-Smith, Cramer-Lakshmikantham, Lakshmikantham-Leela and Ding are improved and generalized by these theorems.