This article addresses a novel anomalous relaxation model with the new general fractional derivative of Sonine kernel. operator is considered in sense proposed work [Yang et al., General derivatives applications viscoelasticity, Academic Press, New York, USA, 2020]. The solution mathematical obtained aid Laplace transform. comparison among classical and models discussed detail. result as tool t...

We begin with an introduction to a calculus of fractional finite differences. We extend the discrete Laplace transform to develop a discrete transform method. We define a family of finite fractional difference equations and employ the transform method to obtain solutions. AMS subject classification: 39A12, 26A33.

The sub-title of this presentation could be “The fractional order integrator approach”. Although fractional order differentiation is commonly considered as the basis of fractional calculus, its effective basis is in fact fractional order integration, mainly because definitions, calculation and properties of fractional derivatives and Fractional Differential Systems (FDS) rely deeply on fraction...

In this paper, the Adomian decomposition method was employed successfully to solve Kudryashov-Sinelshchikov equation involving He?s fractional derivatives, and an approximate analytical solution obtained.

In this article, the electro-osmotic flow of Oldroyd-B fluid in a circular micro-channel with slip boundary condition is considered. The corresponding fractional system is represented by using a newly defined time-fractional Caputo-Fabrizio derivative without singular kernel. Closed form solutions for the velocity field are acquired by means of Laplace and finite Hankel transforms. Additionally...

Most physical phenomena are formulated in the form of non-linear fractional partial differential equations to better understand complexity these phenomena. This article introduces a recent attractive analytic-numeric approach investigate approximate solutions for nonlinear time by means coupling Laplace transform operator and Taylor’s formula. The validity applicability used method illustrated ...

Understanding disease dynamics is crucial for accurately predicting and effectively managing epidemic outbreaks. Mathematical modeling serves as an essential tool in such understanding. This study introduces advanced susceptible, infected, recovered, dead (SIRD) model that uniquely considers the evolution of death parameter, alongside susceptibility infection states. accommodates varying enviro...

in this paper, a new identification of the lagrange multipliers by means of the sumudu transform, is employed to  btain a quick and accurate solution to the fractional black-scholes equation with the initial condition for a european option pricing problem. undoubtedly this model is the most well known model for pricing financial derivatives. the fractional derivatives is described in caputo sen...

In this paper, we apply a new method for solving system of partial differential equations within local fractional derivative operators. The approximate analytical solutions are obtained by using the local fractional Laplace variational iteration method, which is the coupling method of local fractional variational iteration method and Laplace transform. Illustrative examples are included to demo...

The differential equation is an that involves the derivative (derivatives) of dependent variable with respect to independent (variables). represents nothing but a rate change, and helps us present relationship between changing quantity change in another quantity. Adomian decomposition method one iterative methods can be used solve equations, both integer fractional order, linear or nonlinear, o...