Abstract The Mittag–Leffler function is universally acclaimed as the Queen function of
fractional calculus. The aim of this work is to survey the key results and applications …

In this survey we stress the importance of the higher transcendental Mittag-Leffler function in
the framework of the Fractional Calculus. We first start with the analytical properties of the …

Physics-informed neural networks (PINNs), introduced in M. Raissi, P. Perdikaris, and G.
Karniadakis, J. Comput. Phys., 378 (2019), pp. 686--707, are effective in solving integer …

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

The Li‐plating behavior of Li‐ion batteries under fast‐charging conditions is elusive due to a
lack of reliable indicators of the Li‐plating onset. In this work, the relaxation time constant of …

The heat equation is parabolic partial differential equation and occurs in the characterization
of diffusion progress. In the present work, a new fractional operator based on the Rabotnov …

General Fractional Derivatives with Applications in Viscoelasticity introduces the newly
established fractional-order calculus operators involving singular and non-singular kernels …

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

This research considers an inverse source problem for fractional diffusion equation that
containing fractional derivative with non-singular and non-local kernel, namely, Atangana …

We introduce a truncated $ M $-fractional derivative type for $\alpha $-differentiable
functions that generalizes four other fractional derivatives types recently introduced by Khalil …