论文标题
关于ψ-闪光分数微分方程的边界值问题
On the Boundary Value Problems of Ψ -Hilfer Fractional Differential Equations
论文作者
论文摘要
在当前的论文中，我们得出了均质和非均匀线性初始值问题（IVP）的比较结果，以$ψ$ - hilfer分数微分方程。在上层和下溶液的存在下，所获得的比较结果以及用于证明线性$ψ$ - hilfer边界值问题（BVP）的溶液的存在和唯一性通过线性非均匀$ψ$ -HILFER IVP的位置。假设存在较低的解决方案$ W_0 $和上部解决方案$ Z_0 $，我们确定了线段$ [w_0，\，z_0] $的非线性$ψ$ -Hilfer bvp的最小和最大解决方案的加权空间$ c_ c_ {1 - \，γ; \;此外，它表明，迭代的PICARD类型序列从下层和上溶液分别收敛到最小和最大的溶液，并且从线段上的任何点开始汇聚到非线性$ψ$ - hilfer bvp的精确溶液。最后，提供了一个示例，以支持我们获得的主要结果。
In the current paper, we derive the comparison results for the homogeneous and non-homogeneous linear initial value problem (IVP) for $Ψ$-Hilfer fractional differential equations. In the presence of upper and lower solutions, the obtained comparison results and the location of roots theorem utilized to prove the existence and uniqueness of the solution for the linear $Ψ$-Hilfer boundary value problem (BVP) through the linear non-homogeneous $Ψ$-Hilfer IVP. Assuming the existence of lower solution $w_0 $ and upper solution $z_0 $, we establish the existence of minimal and maximal solutions for the nonlinear $Ψ$-Hilfer BVP in the line segment $[w_0,\,z_0]$ of the weighted space $C_{1-\,γ;\, Ψ}\left( J,\,\R\right)$. Further, it demonstrated that the iterative Picard type sequences that began with lower and upper solutions respectively converges to a minimal and maximal solutions, and that started with any point on a line segment converge to the exact solution of nonlinear $Ψ$-Hilfer BVP. Finally, an example is provided in support of the main results we acquired.
