scholarly journals Tripled Fixed Points and Existence Study to a Tripled Impulsive Fractional Differential System via Measures of Noncompactness

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 25
Author(s):  
Sina Etemad ◽  
Mohammed M. Matar ◽  
Maria Alessandra Ragusa ◽  
Shahram Rezapour
Keyword(s):  
Fixed Point ◽  
Control Problem ◽  
Fixed Points ◽  
Differential System ◽  
Hausdorff Measures ◽  
Measures Of Noncompactness ◽  
Tripled Fixed Point ◽  
Impulsive Equations ◽  
Fractional Differential System ◽  
Fractional Differential

In this paper, a tripled fractional differential system is introduced as three associated impulsive equations. The existence investigation of the solution is based on contraction principle and measures of noncompactness in terms of tripled fixed point and modulus of continuity. Our results are valid for both Kuratowski and Hausdorff measures of noncompactness. As an application, we apply the obtained results to a control problem.

scholarly journals Positive solutions to n-dimensional $\alpha _{1}+\alpha _{2}$ order fractional differential system with p-Laplace operator

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Tian Wang ◽  
Guo Chen ◽  
Huihui Pang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Laplace Operator ◽  
Positive Solutions ◽  
Differential System ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Integral Boundary ◽  
Fractional Differential System ◽  
Fractional Differential

AbstractIn this paper, we study an n-dimensional fractional differential system with p-Laplace operator, which involves multi-strip integral boundary conditions. By using the Leggett–Williams fixed point theorem, the existence results of at least three positive solutions are established. Besides, we also get the nonexistence results of positive solutions. Finally, two examples are presented to validate the main results.

scholarly journals Positive Solutions to a Coupled Fractional Differential System with p-Laplacian Operator

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Yuehan Liu ◽  
Xiaodi Zhao ◽  
Huihui Pang
Keyword(s):  
Fixed Point ◽  
Positive Solutions ◽  
Differential System ◽  
Fractional Derivatives ◽  
Existence Result ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Laplacian Operator ◽  
Fractional Differential System ◽  
Fractional Differential

In this paper, we consider a fractional differential system with multistrip and multipoint mixed boundary conditions involving p-Laplacian operator and fractional derivatives. The existence result of positive solutions is established by the Leggett-Williams fixed point theorem. Also, an example is presented to illustrate our main result.

Fractional optimal control problem for variable-order differential systems

2017 ◽  
Vol 20 (6) ◽  
Author(s):  
Gaber M. Bahaa
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Differential System ◽  
Time Derivative ◽  
Variable Order ◽  
Fractional Optimal Control Problem ◽  
Fractional Optimal Control ◽  
Fractional Differential System ◽  
Fractional Differential

AbstractIn this paper, we apply the classical control theory to a variable order fractional differential system in a bounded domain. The Fractional Optimal Control Problem (FOCP) for variable order differential system is considered. The fractional time derivative is considered in a Caputo sense. We first study by using the Lax-Milgram Theorem, the existence and the uniqueness of the solution of the variable order fractional differential system in a Hilbert space. Then we show that the considered optimal control problem has a unique solution. The performance index of a (FOCP) is considered as a function of both state and control variables, and the dynamic constraints are expressed by a Partial Fractional Differential Equation (PFDE) with variable order. The time horizon is fixed. Finally, we impose some constraints on the boundary control. Interpreting the Euler-Lagrange first order optimality condition with an adjoint problem defined by means of right fractional Caputo derivative, we obtain an optimality system for the optimal control. Some examples are analyzed in details.

GENERATING 3-D SCROLL GRID ATTRACTORS OF FRACTIONAL DIFFERENTIAL SYSTEMS VIA STAIR FUNCTION

2007 ◽  
Vol 17 (11) ◽  
pp. 3965-3983 ◽  
Author(s):  
WEIHUA DENG
Keyword(s):  
Differential System ◽  
Autonomous System ◽  
Function Approach ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential System ◽  
Linear Autonomous System ◽  
Fractional Differential ◽  
The One ◽  
Number Of Equilibria

This paper discusses the stair function approach for the generation of scroll grid attractors of fractional differential systems. The one-directional (1-D) n-grid scroll, two-directional (2-D) (n × m)-grid scroll and three-directional (3-D) (n × m × l)-grid scroll attractors are created from a fractional linear autonomous system with a simple stair function controller. Being similar to the scroll grid attractors of classical differential systems, the scrolls of 1-D n-grid scroll, 2-D (n × m)-grid scroll and 3-D (n × m × l)-grid scroll attractors are located around the equilibria of fractional differential system on a line, on a plane or in 3D, respectively and the number of scrolls is equal to the corresponding number of equilibria.

scholarly journals Stability results for the linear degenerate fractional differential system

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Zhixin Zhang ◽  
Jia-Bao Liu ◽  
Jinde Cao ◽  
Wei Jiang ◽  
Ahmed Alsaedi ◽  
...  
Keyword(s):  
Differential System ◽  
Fractional Differential System ◽  
Fractional Differential ◽  
Stability Results ◽  
Linear Degenerate

scholarly journals Hyers–Ulam stability of a coupled system of fractional differential equations of Hilfer–Hadamard type

2019 ◽  
Vol 52 (1) ◽  
pp. 283-295 ◽  
Author(s):  
Manzoor Ahmad ◽  
Akbar Zada ◽  
Jehad Alzabut
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Coupled System ◽  
Ulam Stability ◽  
Fractional Differential System ◽  
Different Types ◽  
Fractional Differential

AbstractIn this paper, existence and uniqueness of solution for a coupled impulsive Hilfer–Hadamard type fractional differential system are obtained by using Kransnoselskii’s fixed point theorem. Different types of Hyers–Ulam stability are also discussed.We provide an example demonstrating consistency to the theoretical findings.

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