We study epidemic Susceptible–Infected–Susceptible (SIS) models in the fractional setting. The novelty is to consider which susceptible and infected populations evolve according different orders. a model based on Caputo derivative, for we establish existence results of solutions. Furthermore, investigate Caputo–Fabrizio operator, provide solutions equilibria. Both can be framed context SIS with...

Noether theorems for two fractional singular systems are discussed. One system involves mixed integer and Caputo derivatives, the other only derivatives. Firstly, primary constraints constrained Hamilton equations given. Then, of established, including identities, quasi-identities conserved quantities. Finally, results obtained illustrated by examples.

The equivalent system for a multiple-rational-order (MRO) fractional differential system is studied, where the fractional derivative is in the sense of Caputo or Riemann-Liouville. With the relationship between the Caputo derivative and the generalized fractional derivative, we can change the MRO fractional differential system with a Caputo derivative into a higher-dimensional system with the s...

In this paper, a time-space fractional diffusion equation in two dimensions (TSFDE2D) with homogeneous Dirichlet boundary conditions is considered. The TSFDE-2D is obtained from the standard diffusion equation by replacing the first-order time derivative with the Caputo fractional derivative tD γ ∗ , γ ∈ (0, 1), and the second order space derivatives with the fractional Laplacian −(−∆)α/2, α ∈ ...

Stability of the solutions to a nonlinear impulsive Caputo fractional differential equation is studied using Lyapunov like functions. The derivative of piecewise continuous Lyapunov functions among the nonlinear impulsive Caputo differential equation of fractional order is defined. This definition is a natural generalization of the Caputo fractional Dini derivative of a function. Several suffic...

Dynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order stochastic delay differential equations driven by Brownian motion. The fractional derivatives are considered in the Caputo sense...

This article compares conformable fractional Derivative with Riemann-Liouville and Caputo derivative by comparing solutions to ordinary differential equations involving the three derivatives via numerical simulations of solutions. The result shows that can be used as an alternative for order α 1/2<α<1.

The Cauchy problem is considered for a homogeneous Hamilton–Jacobi equation with fractional-order coinvariant derivatives, which arises in problems of dynamic optimization systems described by differential equations Caputo fractional derivatives. A generalized solution the minimax sense defined. It proved that such exists, unique, depends continuously on parameters problem, and consistent class...