Dealing with nonsingular kernels is not an easy task due to their restrictions at origin. In this
short paper, we suggest an extension of the fractional operator involving the Mittag-Leffler …

We present a survey on inequalities in fractional calculus that have proven to be very useful
in analyzing differential equations. We mention in particular, a “Leibniz inequality” for …

In this paper we study linear and nonlinear fractional diffusion equations with the Caputo
fractional derivative of non-singular kernel that has been launched recently (Caputo and …

As the title of the book indicates, this is primarily a book on partial differential equations
(PDEs) with two definite slants: toward inverse problems and to the inclusion of fractional …

A two-point boundary value problem whose highest order term is a Caputo fractional
derivative of order δ∈(1, 2) is considered. Al-Refai's comparison principle is improved and …

In this paper, the initial-boundary-value problems for linear and non-linear multi-term
fractional diffusion equations with the Riemann–Liouville time-fractional derivatives are …

Due to the complexly natural attributes of technical systems, reality has been shown that
many systems could be modeled more precisely if they are modeled by using fractional …

In this paper, the initial-boundary-value problems for the one-dimensional linear and non-
linear fractional diffusion equations with the Riemann-Liouville time-fractional derivative are …

It is well known that a continuously differentiable function is monotone in an interval [a, b] if
and only if its first derivative does not change its sign there. We prove that this is equivalent …

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 …