# 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.

## 9 Citations

### 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,…

### 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 ( ψ, ϕ ) -Contractions and Their Application to Fractional Diﬀerential Equations

- Materials Science
- 2020

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

### Existence and Uniqueness of Solutions for Boundary Value Problems of Fractional Diﬀerential Equations with Caputo-Hadamard Derivative 1

- Mathematics
- 2022

In this paper, we are established the existence of positive solutions and uniqueness of a general class of nonlinear Caputo-Hadamard fractional diﬀerential equations in Banach’s space. To ﬁnd the…

### 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, Computer Science
- 2016

In this paper the concept of fuzzy equitable associate graph is introduced and some interesting results are obtained for this new parameter in fuzzy equitable associates graph.

### 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
…

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

- MathematicsAdvances in Difference Equations
- 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…

## References

SHOWING 1-10 OF 26 REFERENCES

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

- MathematicsAppl. Math. Lett.
- 2010

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

- MathematicsComput. Math. Appl.
- 2011

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

- MathematicsComput. Math. Appl.
- 2009

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

- MathematicsComput. Math. Appl.
- 2012

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

- Mathematics
- 2005

### 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,…

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

- Mathematics
- 2008

In this paper we give sufficient conditions for the existence of at least one and at least three positive solutions to the nonlinear fractional boundary value problem Du + a(t)f(u) = 0, 0 < t < 1,1 <…

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

- MathematicsAppl. Math. Lett.
- 2009

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

- MathematicsAppl. Math. Comput.
- 2004

### Solvability of a two-point fractional boundary value problem

- Mathematics
- 2012

The aim of this paper is the study of the existence and uniqueness of solutions for a two-point fractional boundary value problem, by means of Banach contraction principle and Leray Schauder…