Over the past few decades, there has been substantial interest in evolution equations that
involve a fractional-order derivative of order α∈(0, 1) in time, commonly known as …

Fractional differential equations (FDES), ie, differential equations involving fractional-order
derivatives, have received much recent attention in engineering, physics, biology and …

In this paper we investigate the following fractional order in time Cauchy problem D t α u (t)+
A u (t)= f (u (t)), 1< α< 2, u (0)= u 0, u′(0)= u 1. The fractional in time derivative is taken in …

Let Ω⊂R^N be a bounded domain with a Lipschitz continuous boundary. We study the
controllability of the space-time fractional diffusive equation {\mathbbD_t^αu+ …

A focused summary of one-and two-dimensional models for linear and nonlinear wave
propagation in fractional media is given. The basic models, which represent fractional …

Time-fractional partial differential equations are nonlocal-in-time and show an innate
memory effect. Previously, examples like the time-fractional Cahn-Hilliard and Fokker …

On existence and regularity of a terminal value problem for the time fractional diffusion equation
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In the present paper, we study the Cauchy-Dirichlet problem to a nonlocal nonlinear
diffusion equation with polynomial nonlinearities D 0| t α u+(-Δ) psu= γ| u| m-1 u+ μ| u| q-2 u …

The solution of the nonlinear initial-value problem for with, where is the Caputo derivative of
order and are positive parameters, is known to exhibit decay as. No corresponding result for …

This article deals with the initial-boundary value problem for a moderately coupled system of
time-fractional diffusion equations. Defining the mild solution, we establish fundamental …