In this paper, we discuss a new general formulation of fractional optimal control problems whose performance index is in the integral form and dynamics are given by set differential equations Caputo sense. The approach use to prove necessary conditions optimality Pontryagin maximum principle for nonlinear context. Moreover, method based on generalization Mittag–Leffler function used solving class problems. A simple example provided illustrate effectiveness our main result. Copyright © 2016...

This work presents a comprehensive mathematical analysis of the chickenpox transmission model, including positivity, existence, invariant region, and uniqueness solution. We enhance model by introducing optimal control measures using two time‐dependent variables: prevention like vaccination movement constraints, isolation quarantine. The study evaluates basic reproduction number , equilibrium points, stability. New contributions include model’s bifurcations proof existence Fleming’s theorem....

In this research, we introduced a mathematical simulation that describes the transmission dynamics of potato leaf‐roll virus (PLRV) and involves some control measures to eliminate propagation PLRV disease. The proposed model consists four ordinary differential equations divided into two categories: host (potato plant) vector ( Myzus persicae insect). We also split plant subgroups, such as susceptible infected, well vector. examined analysis for models positivity, invariant region, existence,...

<abstract><p>In this article, we considered the nonlinear time-fractional Jaulent–Miodek model (FJMM), which is applied to modeling many applications in basic sciences and engineering, especially physical phenomena such as plasma physics, fluid dynamics, electromagnetic waves media, other applications. The Caputo fractional derivative (CFD) was express operator mathematical formalism of FJMM. We implemented modified generalized Mittag-Leffler method (MGMLFM) show analytical...

In this paper, we use Mittag—Leffler function method for solving some nonlinear fractional differential equations. A new solution is constructed in power series. The derivatives are described by Caputo's sense. To illustrate the reliability of method, examples provided.

In this work, we aim to propose a mathematical formalism for the human liver involving Caputo fractional derivative (CFD) with modified parameters. Regarding proposed order model (FOM), positivity and boundedness theory of an explicit solution are established by using mean-value theorem in sense Caputo. addition, validation FOM is provided ensure that it complies medical interpretation also discuss stability unique equilibrium point (EP) presented model. We apply Generalized Mittag–Leffler...

The objective of this work is to implement two efficient techniques, namely, the Laplace Adomian decomposition method (LADM) and modified generalized Mittag–Leffler function (MGMLFM) on a system nonlinear fractional partial differential equations (NFPDEs) get an analytic-approximate solution. time-fractional Schrödinger equation (TFSE) coupled order Schrödinger-Korteweg-de Vries (Sch-KdV) are found in various areas such as quantum mechanics physics. These describe different types wave...

According to the World Health Organization (WHO), Chronic Heart Disease (CHD) is one of greatest defies currently confronting humankind which sweeping whole globe, with an expanding trend in developing countries. In this paper, a mathematical model (MM) was proposed study connection between fish consumption and CHD mortality Egypt, by considering system ordinary differential equations (ODEs) involving time-fractional derivative (FD). We considered here on Egypt for ease obtaining real data,...

In this work, we present a modified generalized Mittag–Leffler function method (MGMLFM) and Laplace Adomian decomposition (LADM) to get an analytic-approximate solution for nonlinear systems of partial differential equations (PDEs) fractional-order in the Caputo derivative. We apply MGMLFM LADM on time-fractional PDEs. Precisely, consider some important systems, namely Broer–Kaup (BK) Burgers, which have found major significance because they arise many physical applications such as shock...

One of the greatest challenges facing humankind nowadays is to confront that emerging virus, which Coronavirus (COVID-19), and therefore all organizations have unite in order tackle transmission risk this virus. From standpoint, scientific researchers find good mathematical models do describe such virus contribute reducing it one way or another, where study COVID-19 dynamics by very important for analyzing controlling disease propagation. Thus, current work, we present a new fractional-order...

The goal of this study is to derive new conditions that improve the testing oscillatory and asymptotic features fourth-order differential equations with an advanced neutral term. By using Riccati techniques comparison lower-order equations, we establish criteria verify absence positive solutions and, consequently, oscillation all investigated equation. Using our results analyze a few specific instances examined equation, can ultimately clarify significance inequalities. Our are extension...

A challenging SIR epidemiological dynamic model with harmonic rate of incidence and nonlinear recovery is developed to examine the effects available beds in hospitals intervention decrease upon propagation viral disease. The incorporation mean as an novelty present manuscript. assumed less sensitive larger values variables proves more advantageous for highly skewed data compared bi-linear monod types rates. For model's stability, precise mathematical conclusions have been produced. has two...