Nonlocal Boundary Value Problem for Generalized Hilfer Implicit Fractional Differential Equations

On the Impulsive Implicit $Ψ$--Hilfer Fractional Differential Equations with Delay

In this paper, we investigate the existence and uniqueness of solutions and derive the Ulam--Hyers--Mittag--Leffler stability results for impulsive implicit $Ψ$--Hilfer fractional differential equations with time delay. It is demonstrated that the Ulam--Hyers and generalized Ulam--Hyers stability are the specific cases of Ulam--Hyers--Mittag--Leffler stability. Extended version of Gronwall inequality, abstract Gronwall lemma and Picard operator theory are the primary devices in our investigation. We give an example to illustrate the obtained results.

On the Nonlinear Impulsive $Ψ$--Hilfer Fractional Differential Equations

In this paper, we consider the nonlinear $Ψ$-Hilfer impulsive fractional differential equation. Our main objective is to derive the formula for the solution and examine the existence and uniqueness of results. The acquired results are extended to the nonlocal $Ψ$-Hilfer impulsive fractional differential equation. We gave an applications to the outcomes we procured. Further, examples are provided in support of the results we got.

Mathematical Analysis of Nonlocal PDEs for Network Generation

In this paper, we study a certain class of nonlocal partial differential equations (PDEs). The equations arise from a key problem in network science, i.e., network generation from local interaction rules, which result in a change of the degree distribution as time progresses. The evolution of the generating function of this degree distribution can be described by a nonlocal PDE. To address this equation we will rigorously convert it into a local first order PDE. Then, we use theory of characteristics to prove solvability and regularity of the solution. Next, we investigate the existence of ste…

保持结构的空间离散化：用于端口哈密顿系统微分和非局部本构关系

Structure-preserving space discretization of differential and nonlocal constitutive relations for port-Hamiltonian systems

本文研究了端口哈密顿系统中微分本构关系的保持结构空间离散化，通过斯托克斯-拉格朗日结构将其转化为有限维拉格朗日子空间，同时展示了非局部本构关系的扩展应用。

利用拉格朗日描述子揭示分数阶微分方程描述的动力学系统的相空间结构：在杜芬振子中的应用

Using Lagrangian descriptors to reveal the phase space structure of dynamical systems described by fractional differential equations: Application to the Duffing oscillator

本文利用拉格朗日描述子研究分数阶杜芬振子的相空间结构，比较两种分数阶导数实现及两种后向积分方法，论证非局部隐式逆方法能正确揭示分数阶动力学系统的相空间特征。