In this article, we study some class of fractional differential equations involving the Caputo fractional derivative. By using a fixed point theorem on topological degree for condensing maps via a priori estimate method, some sufficient conditions for the existence of solutions are presented. Uniqueness and data dependence results of solutions are also deduced.

Study in Fractional Differential Equations by Means of Topological Degree Methods

In this article, we investigate existence and uniqueness of positive solutions to coupled systems of multi-point boundary value problems for fractional order differential equations of the form $$ \left \{ \textstyle\begin{array}{l} D^{\alpha} x(t)=\phi(t,x(t),y(t)), \quad t\in I=[0,1], \\ D^{\beta} y(t)=\psi(t,x(t),y(t)),\quad t\in I=[0,1], \\ x(0)=g(x),\qquad x(1)=\delta x(\eta),\quad 0< \eta< 1, \\ y(0)=h(y),\qquad y(1)=\gamma y(\xi),\quad 0< \xi< 1, \end{array}\displaystyle \right . $$
 where $\alpha, \beta\in(1,2]$
 , D denotes the Caputo fractional derivative, $0<\delta, \gamma<1$
 are parameters such that $\delta\eta^{\alpha}<1$
 , $\gamma\xi^{\beta}<1$
 , $h, g\in C(I,\mathbb{R})$
 are boundary functions and $\phi,\psi:I\times\mathbb{R} \times \mathbb{R} \rightarrow\mathbb{R}$
 are continuous. We use the technique of topological degree theory to obtain sufficient conditions for existence and uniqueness of positive solutions to the system. Finally, we provide an example to illustrate our main results.

/pdf/degree-theory-and-existence-of-positive-solutions-to-coupled-34s8u84pzc.pdf

Degree theory and existence of positive solutions to coupled systems of multi-point boundary value problems

The aim of this article is to seek some adequate conditions via a prior estimate method (topological degree method) to derive the existence of solution to a nonlinear boundary value problem of frac...

Investigating a Class of Nonlinear Fractional Differential Equations and Its Hyers-Ulam Stability by Means of Topological Degree Theory

In this article, we study existence and uniqueness results for a coupled system of nonlinear fractional order differential subject to nonlinear more general four-point boundary condition of the following type where 0 < α, β ≤ 1 and f, g ∈ C([0, 1] × ℝ2, ℝ) are continuous and the nonlocal functions ϕ, ψ: (I, ℝ) → ℝ are also continuous. The parameters η, ξ satisfy 0 < η < 1, 0 < ξ < 1, and λi, γi, μi(i = 1, 2) are real numbers. Some new existence and uniqueness results are developed for the coupled system using topological degree theory and some standard fixed point theorems. An example is also provided to illustrate our main result.

Existence and Uniqueness Results to a Coupled System of Fractional Order Boundary Value Problems by Topological Degree Theory

Stability analysis for a nonlinear coupled system of fractional hybrid delay differential equations

In this paper, we study the existence and uniqueness of fractional dierential equations with boundary value conditions. A new generalized singular type Gronwall in- equality is given to obtain important a priori bounds. Existence and uniqueness results of solutions are established by virtue of fractional calculus and fixed point method under some weak conditions. An example is given to illustrate the results.

/pdf/existence-and-uniqueness-results-for-fractional-differential-sw1hvebqbu.pdf

Existence and uniqueness results for fractional differential equations with boundary value conditions

/pdf/differential-equations-of-fractional-order-alpha-in-2-3-with-47wjwr07yq.pdf

Differential equations of fractional order $\alpha\in (2,3)$ with boundary value conditions in abstract Banach spaces

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Existence and uniqueness results for fractional differential equations with boundary value conditions

Differential equations of fractional order $\alpha\in (2,3)$ with boundary value conditions in abstract Banach spaces