Solitons propagation dynamics in a saturable PT-symmetric fractional medium

In the current research, the propagation of solitons in a saturable PT-symmetric fractional system is studied by solving nonlinear fractional Schrödinger equation. Three numerical methods are employed for this purpose, namely Monte Carlo based Euler-Lagrange variational schema, split-step method, and extrapolation approach. The results show good agreement and accuracy. The effect of different parameters such as potential depth, Levy indices, and saturation parameter, on the physical properties of the systems such as maximum intensity and soliton width oscillations are considered.

Integral Representation of the Solutions for Neutral Linear Fractional System with Distributed Delays

In the present paper, first we obtain sufficient conditions for the existence and uniqueness of the solution of the Cauchy problem for an inhomogeneous neutral linear fractional differential system with distributed delays (even in the neutral part) and Caputo type derivatives, in the case of initial functions with first kind discontinuities. This result allows to prove that the corresponding homogeneous system possesses a fundamental matrix C(t,s) continuous in t,t∈[a,∞),a∈R. As an application, integral representations of the solutions of the Cauchy problem for the considered inhomogeneous systems are obtained.

A discussion concerning the existence results for the Sobolev-type Hilfer fractional delay integro-differential systems

The goal of this study is to propose the existence results for the Sobolev-type Hilfer fractional integro-differential systems with infinite delay. We intend to implement the outcomes and realities of fractional theory to obtain the main results by Monch’s fixed point technique. Moreover, we show the existence and controllability of the thought about the fractional system with the nonlocal condition. In addition, an application to illustrate the outcomes is also included.

Fractional dynamic system simulating the growth of microbe

There are different approaches that indicate the dynamic of the growth of microbe. In this research, we simulate the growth by utilizing the concept of fractional calculus. We investigate a fractional system of integro-differential equations, which covers the subtleties of the diffusion between infected and asymptomatic cases. The suggested system is applicable to distinguish the presentation of growth level of the infection and to approve if its mechanism is positively active. An optimal solution under simulation mapping assets is considered. The estimated numerical solution is indicated by employing the fractional Tutte polynomials. Our methodology is based on the Atangana–Baleanu calculus (ABC). We assess the recommended system by utilizing real data.

Differential Transform Method as an Effective Tool for Investigating Fractional Dynamical Systems

This study investigates the use of the differential transform method (DTM) for integrating the Rössler system of the fractional order. Preliminary studies of the integer-order Rössler system, with reference to other well-established integration methods, made it possible to assess the quality of the method and to determine optimal parameter values that should be used when integrating a system with different dynamic characteristics. Bifurcation diagrams obtained for the Rössler fractional system show that, compared to the RK4 scheme-based integration, the DTM results are more resistant to changes in the fractionality of the system.

A Proposed High-Gain Observer for a Class of Nonlinear Fractional-Order Systems

This paper proposes a high-gain observer for a class of nonlinear fractional-order systems. Indeed, this approach is based on Caputo derivative to solve the estimation problem for nonlinear systems. The proposed high-gain observer is used to estimate the unknown states of a nonlinear fractional system. The use of Lyapunov convergence functions to establish stability of system is detailed. The influence of different fractional orders on the estimation is presented. Ultimately, numerical simulation examples demonstrate the efficiency of the proposed approach.

A Comparative Analysis of Fractional-Order Gas Dynamics Equations via Analytical Techniques

This article introduces two well-known computational techniques for solving the time-fractional system of nonlinear equations of unsteady flow of a polytropic gas. The methods suggested are the modified forms of the variational iteration method and the homotopy perturbation method by the Elzaki transformation. Furthermore, an illustrative scheme is introduced to verify the accuracy of the available techniques. A graphical representation of the exact and derived results is presented to show the reliability of the suggested approaches. It is also shown that the findings of the current methodology are in close harmony with the exact solutions. The comparative solution analysis via graphs also represents the higher reliability and accuracy of the current techniques.

Iterative Learning Control for Fractional order Nonlinear System with Initial Shift

In this study, a closed-loop Dα -type iterative learning control(ILC) with a proportional D-type iterative learning updating law for the initial shift is applied to nonlinear conformable fractional system. First, the system with the initial shift is introduced. Then, fractional-order ILC (FOILC) frameworks that experience the initial shift problem for the path-tracking of nonlinear conformable fractional order systems are addressed. Moreover, the sufficient condition for the convergence of tracking errors is obtained in the time domain by introducing λ -norm and Hölder’s inequality. Lastly, numerical examples are provided to illustrate the effectiveness of the proposed methods.