General Fractional Derivatives: Theory, Methods and Applications provides knowledge of
the special functions with respect to another function, and the integro-differential operators …

Trapped dynamics widely appears in nature, eg, the motion of particles in viscous
cytoplasm. The famous continuous time random walk (CTRW) model with power law waiting …

We investigate the Hilfer-type operator within the topic of tempered fractional calculus with
respect to functions. This operator, the tempered Ψ-Hilfer derivative, is defined for the first …

The prime aim of the present paper is to continue developing the theory of tempered
fractional integrals and derivatives of a function with respect to another function. This theory …

Let us now consider the Fokker-Planck equation, which is a partial differential equation that
describes the time evolution of the PDF of the positions of particles, and was introduced in …

In this paper, we develop a new technique known as Tempered Fractional 𝕁-Transform (TF
𝕁 T). This scheme can be applied to study numerous linear and nonlinear dynamical …

Functionals of Brownian and non-Brownian motions have diverse applications and attracted
a lot of interest among scientists. This paper focuses on deriving the forward and backward …

In this work, we extend the fractional linear multistep methods in C. Lubich, SIAM J. Math.
Anal., 17 (1986), pp. 704--719 to the tempered fractional integral and derivative operators in …

This paper studies the problem of partial topology identification of tempered fractional
complex networks. By tempered fractional calculus theory and pinning controlling …

For a class of tempered fractional integro-differential equation of the Caputo type, a
comparative study of three numerical schemes is presented in this paper. The schemes …