关于分数动力学方程

一类含广义k-Bessel函数的分数阶动力学方程

Certain Fractional Kinetic Equations Involving Generalized k-Bessel Function

本文给出了含广义k-Bessel函数的分数阶动力学方程的一种新的进一步推广形式。本文从分数动力学方程的解出发，讨论了广义k-Bessel函数的流形一般性。这里得到的结果是相当普遍的性质，能够产生大量的已知和（可能）新的结果。

分数阶动力学方程及其基于Sumudu变换多参数Struve函数的解

On fractional kinetic equations and their Sumudu transform multiparameter Struve functions based solutions

本文利用Sumudu变换算子处理分数阶动力学方程。得到的精确解用四参数Struve函数表示。通过求解的方法，根据Sumudu性质，给出了一些新颖的、有用的和新颖的动力学定理。在这项研究中获得的结果可以务实地用于许多分支的理论和实验科学的应用，而不是最不重要的是数学物理，和各种工程领域。

序列共形分数阶微分方程和共形分数阶Hermite微分方程的解

Solutions of Sequential Conformable Fractional Differential Equations around an Ordinary Point and Conformable Fractional Hermite Differential Equation

本文给出了2α阶齐次序列线性协调分数阶微分方程在变系数情形下在常点附近的幂级数解.在此基础上，介绍了共形分数阶Hermite微分方程、共形分数阶Hermite多项式及其基本性质。

Solution to the fractional equation with left-sided fractional Bessel derivatives of Gerasimov-Caputo type

In the article we propose and study a method to solve ordinary differential equations with left-sided fractional Bessel derivatives on semi-axes of Gerasimov-Caputo type. We derive explicit solutions to equations with fractional powers of Bessel operator using the Meijer integral transform.

保形分数阶Bessel方程与Bessel函数

Conformable Fractional Bessel Equation and Bessel Functions

本文研究了共形分数阶Bessel微分方程和分数阶Bessel函数在正则奇点x=0附近的分数阶幂级数解.然后，我们比较了分数阶解和普通解。此外，我们还给出了分数阶Bessel函数的一些性质。

On a Hilfer fractional differential equation with nonlocal Erdélyi-Kober fractional integral boundary conditions

We consider a Hilfer fractional differential equation with nonlocal Erdélyi-Kober fractional integral boundary conditions. The existence, uniqueness and Ulam-Hyers stability results are investigated by means of the Krasnoselskii's fixed point theorem and Banach's fixed point theorem. An example is given to illustrate the main results.

Mittag-Leffler非Singular Kernel的Caputo分数阶微分方程：比较原理及应用

Fractional Differential Equations Involving Caputo Fractional Derivative with Mittag-Leffler Non-Singular Kernel: Comparison Principles and Applications

本文研究了具有$0<α<1.$阶Mittag-Leffler非奇异核的含有Caputo分数阶导数的线性和非线性分数阶微分方程.首先得到了函数在极值点处的分数阶导数的一个新的估计，并得到了线性分数阶微分方程解存在的一个必要条件.所得到的充分条件确定了相应的分数阶初值问题的初始条件。然后，我们推导出比较原则的线性分式方程。应用这些原理得到了线性方程解的范数估计和非线性方程解的唯一性结果。我们还得到了非线性方程的解的上下界上界。通过几个例子说明了新结果的适用性。

Existence results for a class of Caputo type fractional differential equations with Riemann-Liouville fractional integrals and Caputo fractional derivatives in boundary conditions

In this paper, we investigate the existence and uniqueness of solutions for a fractional boundary value problem supplemented with nonlocal Riemann-Liouville fractional integral and Caputo fractional derivative boundary conditions. Our results are based on some known tools of fixed point theory. Finally, some illustrative examples are included to verify the validity of our results.

A new fractional derivative of variable order with non-singular kernel and fractional differential equations

In this paper, we introduce two new non-singular kernel fractional derivatives and present a class of other fractional derivatives derived from the new formulations. We present some important results of uniformly convergent sequences of continuous functions, in particular the Comparison's principle, and others that allow, the study of the limitation of fractional nonlinear differential equations.

On a New Class of Fractional Calculus of Variations and Related Fractional Differential Equations

This paper is concerned with analyzing a class of fractional calculus of variations problems and their associated Euler-Lagrange (fractional differential) equations. Unlike the existing fractional calculus of variations which is based on the classical notion of fractional derivatives, the fractional calculus of variations considered in this paper is based on a newly developed notion of weak fractional derivatives and their associated fractional order Sobolev spaces. Since fractional derivatives are direction-dependent, using one-sided fractional derivatives and their combinations leads to new …