Asymptotically almost periodic solutions of fractional relaxation inclusions with Caputo derivatives

The existence and uniqueness of almost periodic and asymptotically almost periodic solutions of semilinear Cauchy inclusions

The main aim of this paper is to investigate almost periodicity and asymptotic almost periodicity of abstract semilinear Cauchy inclusions of first order with (asymptotically) Stepanov almost periodic coefficients. To achieve our goal, we employ fixed point theorems and the well known results on the generation of infinitely differentiable degenerate semigroups with removable singularites at zero.

Almost automorphic and asymptotically almost automorphic type functions in Lebesgue spaces with variable exponents $L^{p(x)}$

The paper introduces and studies the class of (asymptotically) Stepanov almost automorphic functions with variable exponents. Any function belonging this class needs to be (asymptotically) Stepanov almost automorphic. A few relevant applications to abstract Volterra integro-differential inclusions in Banach spaces is presented.

Asymptotically Weyl almost periodic functions in Lebesgue spaces with variable exponents

In this paper, we introduce and analyze several different notions of Weyl almost periodic functions and Weyl ergodic components in Lebesgue spaces with variable exponent $L^{p(x)}.$ We investigate the invariance of (asymptotical) Weyl almost periodicity with variable exponent under the actions of convolution products, providing also some illustrative applications to abstract fractional differential inclusions in Banach spaces. The introduced classes of generalized (asymptotically) Weyl almost periodic functions are new even in the case that the function $p(x)$ has a constant value $p\geq 1,$ p…

Composition principles for generalized almost periodic functions

In this paper, we consider composition principles for generalized almost periodic functions. We prove several new composition principles for the classes of (asymptotically) Stepanov $p$-almost periodic functions and (asymptotically, equi-)Weyl $p$-almost periodic functions, where $1\leq p<\infty ,$ and explain how we can use some of them in the qualitative analysis of solutions for certain classes of abstract semilinear Cauchy inclusions in Banach spaces.

分数阶流动方程。油井压力亏损的模型

Fractional flow equations. A model for pressure deficit in an oil well

本文提出一种基于分数阶导数的流动方程系统，用于模拟由岩石骨架、孔洞介质和裂缝构成的三重连续介质储层的压力亏损，并利用 Caputo 分数阶导数的 Laplace 变换和 Bessel 函数求得了 Laplace 空间中的半解析解。