# Application of Schauder fixed point theorem to a coupled system of differential equations of fractional order

@article{Hao2014ApplicationOS, title={Application of Schauder fixed point theorem to a coupled system of differential equations of fractional order}, author={Mengru Hao and Chengbo Zhai}, journal={The Journal of Nonlinear Sciences and Applications}, year={2014}, volume={07}, pages={131-137} }

In this paper, by using Schauder xed point theorem, we study the existence of at least one positive solution to a coupled system of fractional boundary value problems given by D 1 0+y1(t) = 1a1(t)f(t;y1(t);y2(t)) +e1(t); D 2 0+y2(t) = 2a2(t)g(t;y1(t);y2(t)) +e2(t); where 1; 22 (n 1;n] for n > 3 and n2 N, subject to the boundary conditions y (i) 1 (0) = 0 = y (i) 2 (0), for 0 i n 2, and [D 0+y1(t)]t=1 = 0 = [D 0+y2(t)]t=1, for 1 n 2.

## 7 Citations

Unique solutions for a new coupled system of fractional differential equations

- Mathematics
- 2018

AbstractIn this article, we discuss a new coupled system of fractional differential equations with integral boundary conditions
…

Positive solutions for singular coupled integral boundary value problems of nonlinear Hadamard fractional differential equations

- Mathematics
- 2015

In this paper, we study the existence of positive solutions for a class of coupled integral boundary value problems of nonlinear semipositone Hadamard fractional differential equations Du(t) + λf(t,…

Local uniqueness of positive solutions for a coupled system of fractional differential equations with integral boundary conditions

- Mathematics
- 2017

In this paper, we study a coupled system of fractional boundary value problems subject to integral boundary conditions. By applying a recent fixed point theorem in ordered Banach spaces, we…

Existence of positive solution to the boundary value problems for coupled system of nonlinear fractional differential equations

- MathematicsAIMS Mathematics
- 2019

In this paper, we investigate the existence criteria of at least one positive solution to the three-point boundary value problems with coupled system of Riemann-Liouville type nonlinear fractional…

Some Fixed Point Theorems for $$F(\psi,\varphi)$$-Contractions and Their Application to Fractional Differential Equations

- Mathematics
- 2020

The main object of this paper is to establish some fixed point results for
$$F(\psi,\varphi)$$
-contractions in partially-ordered metric spaces. As an application of one of these fixed point…

Variation of parameters for local fractional nonhomogenous lineardifferential equations

- Mathematics
- 2016

In this paper we study the method of variation of parameters to find a particular solution of a nonhomogenous linear fractional differential equations. A formula similar to that for usual ordinary…

Undetermined coefficients for local fractional differential equations

- Mathematics
- 2016

Let G= (V, σ, μ) be a fuzzy graph. Let H be the graph constructed from G as follows V(H) =V(G), two points u and v are adjacent in H if and only if u and v are adjacent and degree fuzzy equitable in…

## References

SHOWING 1-10 OF 27 REFERENCES

Existence of a positive solution to a class of fractional differential equations

- Mathematics, Computer ScienceAppl. Math. Lett.
- 2010

The Green’s function is derived for this fractional boundary value problem and it is shown that it satisfies certain properties, and cone theoretic techniques are used to deduce a general existence theorem for this problem.

Existence of a positive solution to systems of differential equations of fractional order

- Computer Science, MathematicsComput. Math. Appl.
- 2011

The results here generalize some recent results on both scalar fractional boundaries value problems and systems of fractional boundary value problems, and provide two explicit numerical examples to illustrate the generalizations that the results afford.

Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions

- Computer Science, MathematicsComput. Math. Appl.
- 2009

The Schauder fixed point theorem is applied and an existence result is proved for the following system, where @a,@b,p,q,@h,@c satisfy certain conditions.

Mixed monotone operator methods for the existence and uniqueness of positive solutions to Riemann-Liouville fractional differential equation boundary value problems

- Mathematics
- 2013

AbstractThis work is concerned with the existence and uniqueness of positive solutions for the following fractional boundary value problem:
…

Existence and uniqueness of solutions for a coupled system of multi-term nonlinear fractional differential equations

- Computer Science, MathematicsComput. Math. Appl.
- 2012

By means of Schauder fixed point theorem and Banach contraction principle, an existence result and a unique result for the solution are obtained, respectively.

Positive solutions for boundary value problem of nonlinear fractional differential equation.

- Mathematics
- 2008

Existence of unbounded positive solutions for BVPs of singular fractional differential equations

- Mathematics
- 2012

In this article, we establish the existence of multiple unbounded positive solutions to the boundary value problem of the nonlinear singular fractional differential equation Dα 0+u(t) + f(t,…

Uniqueness of positive solutions for a fractional differential equation via a fixed point theorem of a sum operator

- Mathematics
- 2012

In this work, we study the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary-value problems. Our analysis relies on a fixed point theorem of a sum…

Boundary value problem for a coupled system of nonlinear fractional differential equations

- Mathematics, Computer ScienceAppl. Math. Lett.
- 2009

Abstract In this work we discuss a boundary value problem for a coupled differential system of fractional order. The differential operator is taken in the Riemann–Liouville sense and the nonlinear…

The existence of a positive solution for a singular coupled system of nonlinear fractional differential equations

- Mathematics, Computer ScienceAppl. Math. Comput.
- 2004

The existence of a positive solution to a singular coupled system of nonlinear fractional differential equations based on a nonlinear alternative of Leray-Schauder type and Krasnoselskii's fixed point theorem in a cone is established.