scholarly journals Uniqueness of Solutions for the Initial Value Problem of a Simple Type Riccati Equation with Variable Fractional Order

2021 ◽  
Vol 1995 (1) ◽  
pp. 012056
Author(s):  
Lisha Chen ◽  
Shiyou Lin ◽  
Boyang Li
Keyword(s):  
Riccati Equation ◽  
Fractional Order ◽  
Initial Value Problem ◽  
Simple Type ◽  
Initial Value ◽  
Uniqueness Of Solutions

THE INITIAL VALUE PROBLEM FOR THE DEEP BÉNARD CONVECTION EQUATIONS WITH DATA IN Lq

1996 ◽  
Vol 06 (02) ◽  
pp. 269-277 ◽  
Author(s):  
Z. CHARKI
Keyword(s):  
Fixed Point ◽  
Initial Value Problem ◽  
Existence And Uniqueness ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Bénard Convection ◽  
Benard Convection ◽  
Point Argument

A fixed point argument is used to prove the existence and uniqueness of solutions for the unsteady deep Bénard convection equations in [Formula: see text] for [Formula: see text].

A Numerical Algorithm to Initial Value Problem of Caputo Fractional-Order Differential Equation

2015 ◽  
Author(s):  
Lu Bai ◽  
Dingyü Xue
Keyword(s):  
Differential Equation ◽  
Difference Equation ◽  
Error Analysis ◽  
Numerical Solution ◽  
Fractional Order ◽  
Numerical Algorithm ◽  
Initial Value Problem ◽  
Order Differential Equation ◽  
Fractional Order Differential Equation ◽  
Initial Value

A numerical algorithm is presented to solve the initial value problem of linear and nonlinear Caputo fractional-order differential equations. Firstly, nonzero initial value problem should be transformed into zero initial value problem. Error analysis has been done to polynomial algorithm, the reason has been found why the calculation error of the algorithm is large. A new algorithm called exponential function algorithm is proposed based on the analysis. The obtained fractional-order differential equation is transformed into difference equation. If the differential equation is linear, the obtained difference equation is explicit, the numerical solution can be solved directly; otherwise, the obtained difference equation is implicit, the predictor of the numerical solution can be obtained with extrapolation algorithm, substitute the predictor into the equation, the corrector can be solved. Error analysis has been done to the new algorithm, the algorithm is of first order.

scholarly journals On the initial value problem for causal variational principles

2017 ◽  
Vol 2017 (725) ◽  
Author(s):  
Felix Finster ◽  
Andreas Grotz
Keyword(s):  
Metric Space ◽  
Initial Value Problem ◽  
Existence And Uniqueness ◽  
Variational Principles ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Compact Metric Space ◽  
Continuous Setting

AbstractWe formulate the initial value problem for causal variational principles in the continuous setting on a compact metric space. The existence and uniqueness of solutions is analyzed. The results are illustrated by simple examples.

scholarly journals Existence and Uniqueness of Solutions for Initial Value Problem of Nonlinear Fractional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Qiuping Li ◽  
Shurong Sun ◽  
Ping Zhao ◽  
Zhenlai Han
Keyword(s):  
Differential Equation ◽  
Initial Value Problem ◽  
Existence And Uniqueness ◽  
Upper And Lower Solutions ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Nonlinear Fractional Differential Equation ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential

We discuss the initial value problem for the nonlinear fractional differential equationL(D)u=f(t,u),  t∈(0,1],  u(0)=0, whereL(D)=Dsn-an-1Dsn-1-⋯-a1Ds1,0<s1<s2<⋯<sn<1, andaj<0,j=1,2,…,n-1,Dsjis the standard Riemann-Liouville fractional derivative andf:[0,1]×ℝ→ℝis a given continuous function. We extend the basic theory of differential equation, the method of upper and lower solutions, and monotone iterative technique to the initial value problem. Some existence and uniqueness results are established.

scholarly journals Initial value problem of fractional order

2015 ◽  
Vol 2 (1) ◽  
pp. 1004797 ◽  
Author(s):  
A. Guezane-Lakoud
Keyword(s):  
Fractional Order ◽  
Initial Value Problem ◽  
Initial Value
Sign in / Sign up

Export Citation Format

Share Document