scholarly journals Analysis of a System for Linear Fractional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Fang Wang ◽  
Zhen-hai Liu ◽  
Ping Wang
Keyword(s):  
Differential Equations ◽  
Unique Solution ◽  
Fractional Differential Equations ◽  
Constant Coefficient ◽  
Existence And Uniqueness ◽  
Diagonal Matrix ◽  
Fractional Differential ◽  
Homogeneous Linear ◽  
Linear Fractional Differential Equations

The main purpose of this paper is to obtain the unique solution of the constant coefficient homogeneous linear fractional differential equationsDt0qX(t)=PX(t),X(a)=Band the constant coefficient nonhomogeneous linear fractional differential equationsDt0qX(t)=PX(t)+D,X(a)=BifPis a diagonal matrix andX(t)∈C1-q[t0,T]×C1-q[t0,T]×⋯×C1-q[t0,T]and prove the existence and uniqueness of these two kinds of equations for anyP∈L(Rm)andX(t)∈C1-q[t0,T]×C1-q[t0,T]×⋯×C1-q[t0,T]. Then we give two examples to demonstrate the main results.

Systems of Nonlinear Fractional Differential Equations

2015 ◽  
Vol 18 (1) ◽  
Author(s):  
Tadeusz Jankowski
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Unique Solution ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential ◽  
The Right ◽  
Linear Fractional Differential Equations

AbstractUsing the iterative method, this paper investigates the existence of a unique solution to systems of nonlinear fractional differential equations, which involve the right-handed Riemann-Liouville fractional derivatives $D^{q}_{T}x$ and $D^{q}_{T}y$. Systems of linear fractional differential equations are also discussed. Two examples are added to illustrate the results.

The Solution of Linear Fractional Differential Equations Using the Fractional Meta-Trigonometric Functions

2011 ◽  
Author(s):  
Carl F. Lorenzo ◽  
Rachid Malti ◽  
Tom T. Hartley
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Constant Coefficient ◽  
Laplace Transforms ◽  
New Method ◽  
Trigonometric Functions ◽  
Fractional Differential ◽  
Linear Fractional Differential Equations

A new method for the solution of linear constant coefficient fractional differential equations of any commensurate order based on the Laplace transforms of the fractional meta-trigonometric functions and the R-function is presented. The new method simplifies the solution of such equations. A simplifying characterization that reduces the number of parameters in the fractional meta-trigonometric functions is introduced.

scholarly journals The unique solution of some operator equations via fractional differential equations

2022 ◽  
Vol 40 ◽  
pp. 1-9
Author(s):  
Hojat Afshari ◽  
L. Khoshvaghti
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Unique Solution ◽  
Positive Solutions ◽  
Operator Equation ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Ordered Banach Space ◽  
Operator Equations ◽  
Fractional Differential

In this paper we consider the existence and uniqueness of positive solutions to the following operator equation in an ordered Banach space $E$$$A(x,x)+B(x,x)=x,~x\in P,$$where $P$ is a cone in $E$. We study an application for fractional differential equations.

scholarly journals A Hilbert Space Approach to Fractional Differential Equations

2021 ◽  
Author(s):  
Kai Diethelm ◽  
Konrad Kitzing ◽  
Rainer Picard ◽  
Stefan Siegmund ◽  
Sascha Trostorff ◽  
...  
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Hilbert Spaces ◽  
Existence And Uniqueness ◽  
Fractional Operators ◽  
Uniqueness Of Solutions ◽  
Fractional Differential ◽  
The Fourier Transform ◽  
Linear Fractional Differential Equations ◽  
Space Approach

AbstractWe study fractional differential equations of Riemann–Liouville and Caputo type in Hilbert spaces. Using exponentially weighted spaces of functions defined on $${\mathbb {R}}$$ R , we define fractional operators by means of a functional calculus using the Fourier transform. Main tools are extrapolation- and interpolation spaces. Main results are the existence and uniqueness of solutions and the causality of solution operators for non-linear fractional differential equations.

scholarly journals Multi-term fractional differential equations with nonlocal boundary conditions

2018 ◽  
Vol 16 (1) ◽  
pp. 1519-1536
Author(s):  
Bashir Ahmad ◽  
Najla Alghamdi ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
The Given

AbstractWe introduce and study a new kind of nonlocal boundary value problems of multi-term fractional differential equations. The existence and uniqueness results for the given problem are obtained by applying standard fixed point theorems. We also construct some examples for demonstrating the application of the main results.

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