In this paper we consider a Caputo type fractional derivative with respect to another function.
Some properties, like the semigroup law, a relationship between the fractional derivative …

In the present case, we propose the correct version of the fractional Adams-Bashforth
methods which take into account the nonlinearity of the kernels including the power law for …

This chapter presents an attempt to collate existing data about fractional derivatives with non-
singular kernels conceived by Caputo and Fabrizio in 2015. The idea attracted immediately …

Mathematical analysis with the numerical simulation of the newly formulated fractional
version of the Adams-Bashforth method using the Atangana-Baleanu operator which has …

New approach of fractional derivative with a new local kernel is suggested in this paper. The
kernel introduced in this work is the well-known normal distribution that is a very common …

Recently a new fractional differentiation was introduced to get rid of the singularity in the
Riemann-Liouville and Caputo fractional derivative. The new fractional derivative has then …

In this paper, we obtain analytical solutions for the fractional cubic isothermal auto-catalytic
chemical system with Caputo–Fabrizio and Atangana–Baleanu fractional time derivatives in …

In this work, we present an analysis based on a combination of the Laplace transform and
homotopy methods in order to provide a new analytical approximated solutions of the …

Abstract Recently, Caputo and Fabrizio proposed a new derivative with fractional order
without singular kernel. The derivative has several interesting properties that are useful for …

In this article, we develop an analytical method for solving fractional order partial differential
equations. Our method is the generalizations of homotopy perturbations Laplace transform …