scholarly journals Fractional Stochastic Differential Equations with Hilfer Fractional Derivative: Poisson Jumps and Optimal Control

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Fathalla A. Rihan ◽  
Chinnathambi Rajivganthi ◽  
Palanisamy Muthukumar
Keyword(s):  
Optimal Control ◽  
Fractional Derivative ◽  
Existence And Uniqueness ◽  
Mild Solutions ◽  
Poisson Jumps ◽  
Hilfer Fractional Derivative ◽  
Analysis Techniques ◽  
Mild Conditions ◽  
Fractional Stochastic Differential Equations ◽  
Existence Of Optimal Control

In this work, we consider a class of fractional stochastic differential system with Hilfer fractional derivative and Poisson jumps in Hilbert space. We study the existence and uniqueness of mild solutions of such a class of fractional stochastic system, using successive approximation theory, stochastic analysis techniques, and fractional calculus. Further, we study the existence of optimal control pairs for the system, using general mild conditions of cost functional. Finally, we provide an example to illustrate the obtained results.

scholarly journals Exponential behavior of neutral impulsive stochastic integro-differential equations driven by Poisson jumps and Rosenblatt process

2020 ◽  
Vol 7 (1) ◽  
pp. 1-21
Author(s):  
Ravikumar Kasinathan ◽  
Ramkumar Kasinathan ◽  
Mahamat Hassan Mahamat Hamit ◽  
Mamadou Abdoul Diop
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Resolvent Operator ◽  
Mild Solutions ◽  
Poisson Jumps ◽  
Uniqueness Of Solutions ◽  
Exponential Behavior ◽  
Analysis Techniques ◽  
Rosenblatt Process ◽  
Theoretical Results

AbstractIn this article, we are concerned with the neutral impulsive stochastic integro-differential equations driven by Poisson jumps and Rosenblatt process. By using resolvent operator and some analysis techniques, we ensure existence and uniqueness of solutions. Further, we investigate exponential stability of mild solutions. We have also given an example to illustrate our theoretical results.

scholarly journals Stability Results for Implicit Fractional Pantograph Differential Equations via ϕ-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 94 ◽  
Author(s):  
Idris Ahmed ◽  
Poom Kumam ◽  
Kamal Shah ◽  
Piyachat Borisut ◽  
Kanokwan Sitthithakerngkiet ◽  
...  
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Integral Condition ◽  
Hilfer Fractional Derivative ◽  
Fractional Differential ◽  
Generalized Fractional Derivative ◽  
Stability Results

This paper presents a class of implicit pantograph fractional differential equation with more general Riemann-Liouville fractional integral condition. A certain class of generalized fractional derivative is used to set the problem. The existence and uniqueness of the problem is obtained using Schaefer’s and Banach fixed point theorems. In addition, the Ulam-Hyers and generalized Ulam-Hyers stability of the problem are established. Finally, some examples are given to illustrative the results.

THE EXISTENCE AND UNIQUENESS FOR NON-LIPSCHITZ STOCHASTIC NEUTRAL DELAY EVOLUTION EQUATIONS DRIVEN BY POISSON JUMPS

2009 ◽  
Vol 09 (01) ◽  
pp. 135-152 ◽  
Author(s):  
JIAOWAN LUO ◽  
TAKESHI TANIGUCHI
Keyword(s):  
Existence And Uniqueness ◽  
Initial Function ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Jump Processes ◽  
Poisson Jumps ◽  
Neutral Delay ◽  
Poisson Jump

In this paper, we consider the existence and uniqueness of mild solutions to non-Lipschitz stochastic neutral delay evolution equations driven by Poisson jump processes: [Formula: see text] with an initial function X(s) = φ(s), -r ≤ s ≤ 0, where φ : [-r, 0] → H is a cadlag function with [Formula: see text].

scholarly journals The Neutral Stochastic Integrodifferential Equations with Jumps

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Diem Dang Huan
Keyword(s):  
Successive Approximation ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Mild Solutions ◽  
Integrodifferential Equations ◽  
Poisson Jumps ◽  
Initial Value ◽  
Carathéodory Conditions ◽  
Global And Local ◽  
Continuous Dependence Of Solutions

We study the existence and uniqueness of mild solutions for neutral stochastic integrodifferential equations with Poisson jumps under global and local Carathéodory conditions on the coefficients by means of the successive approximation. Furthermore, we give the continuous dependence of solutions on the initial value. Finally, an example is provided to illustrate the effectiveness of the obtained results.

scholarly journals Existence of Mild Solutions for a Class of Impulsive Hilfer Fractional Coupled Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Karim Guida ◽  
Khalid Hilal ◽  
Lahcen Ibnelazyz ◽  
Ming Mei
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Derivative ◽  
Banach Spaces ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Mild Solutions ◽  
Existence Results ◽  
Coupled Systems ◽  
Hilfer Fractional Derivative

The aim of this paper is to give existence results for a class of coupled systems of fractional integrodifferential equations with Hilfer fractional derivative in Banach spaces. We first give some definitions, namely the Hilfer fractional derivative and the Hausdorff’s measure of noncompactness and the Sadovskii’s fixed point theorem.

scholarly journals Mild Solutions for Impulsive Integro-Differential Equations Involving Hilfer Fractional Derivative with almost Sectorial Operators

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 313
Author(s):  
Kulandhaivel Karthikeyan ◽  
Panjaiyan Karthikeyan ◽  
Nichaphat Patanarapeelert ◽  
Thanin Sitthiwirattham
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Jump Conditions ◽  
Hilfer Fractional Derivative ◽  
Sectorial Operators ◽  
Almost Sectorial Operators ◽  
Suitable Definition ◽  
Definition Of

In this manuscript, we establish the mild solutions for Hilfer fractional derivative integro-differential equations involving jump conditions and almost sectorial operator. For this purpose, we identify the suitable definition of a mild solution for this evolution equations and obtain the existence results. In addition, an application is also considered.

Existence of mild solutions for a class of Hilfer fractional evolution equations with nonlocal conditions

2017 ◽  
Vol 20 (3) ◽  
Author(s):  
Min Yang ◽  
Qiru Wang
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Hilfer Fractional Derivative ◽  
Fractional Evolution Equations ◽  
Noncompact Measure ◽  
The Fixed Point Theorem ◽  
New Criteria

AbstractIn this paper, we consider a class of evolution equations with Hilfer fractional derivative. By employing the fixed point theorem and the noncompact measure method, we establish a number of new criteria to guarantee the existence and uniqueness of mild solutions when the associated semigroup is compact or not.

OPTIMAL HARVESTING PROBLEM FOR AN AGE-DEPENDENT n-DIMENSIONAL COMPETING SYSTEM WITH DIFFUSION

2008 ◽  
Vol 01 (02) ◽  
pp. 133-145 ◽  
Author(s):  
ZHIXUE LUO ◽  
ZE-RONG HE
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Existence And Uniqueness ◽  
Spatial Diffusion ◽  
Optimal Harvesting ◽  
Negative Solution ◽  
Optimal Control Strategy ◽  
Age Dependent ◽  
The Fixed Point Theorem ◽  
Existence Of Optimal Control

In this work, optimal harvesting policy for an age-dependent and spatial diffusion n-dimensional competing species is discussed. The existence and uniqueness of non-negative solution to the system are investigated by using the fixed point theorem. The existence of optimal control strategy is discussed and optimality conditions are obtained. Our results extend some known criteria.

scholarly journals SYARAT CUKUP UNTUK OPTIMALITAS MASALAH KONTROL KUADRATIK LINIER

2013 ◽  
Vol 2 (2) ◽  
pp. 63
Author(s):  
Suci Fratama Sari
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Riccati Equation ◽  
Existence And Uniqueness ◽  
Algebraic Riccati Equation ◽  
Lqr Problem ◽  
Existence Of Optimal Control

The LQR problem is an optimal control problem which is now used in variouselds of science. The optimal control is given by u(t) = 􀀀Kx(t), where K = R􀀀1(PB)Tand P is a unique positive semidenite solution of Algebraic Riccati Equation (ARE).The existence of optimal control u(t) depends on the existence matrix P. In this paper,the sucient conditions which ensures the existence and uniqueness of the optimal con-trol u(t) will be determined. Moreover, some examples as an illustration of the LQRproblem will be given.

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