Search

The work reported in this paper deals with the study of a coupled system for fractional terminal value problems involving ψ-Hilfer fractional derivative. The existence and uniqueness theorems to the problem at hand are investigated. Besides, the stability analysis in the Ulam–Hyers sense of a given system is studied. Our discussion is based upon known fixed point theorems of Banach and Krasnoselskii. Examples are also provided to demonstrate the applicability of our results. [ABSTRACT FROM AUTHOR]

In this paper, we deal with Caputo-type fractional differential inequality where there is a low-order fractional derivative with the term polynomial source. We investigate the nonexistence of nontrivial global solutions in a suitable space via the test function technique and some properties of fractional integrals. Finally, we demonstrate three examples to illustrate our results. The presented results are more general than those in the literature, which can be obtained as particular cases. [ABSTRACT FROM AUTHOR]

Fall armyworm (Spodoptera frugiperda), a highly destructive and fast spreading agricultural pest native to North and South America, poses a real threat to global food security. In this paper, to explore the dynamics and implications of fall armyworm outbreak in a field of maize biomass, we propose a new dynamical system for maize biomass and fall armyworm interaction via Caputo fractional-order operator, which is not only a nonlocal operator but also contains all characteristics concerned with memory of the dynamical system. We define the basic reproduction number, which represents the average number of newborns produced by one individual female moth during its life span. We establish that the basic reproduction number is a threshold quantity, which determines persistence and extinction of the pest. Finally, we simulate the Caputo system using the Adam–Bashforth–Moulton method to illustrate the main results. [ABSTRACT FROM AUTHOR]

This paper investigates a new model on coronavirus-19 disease (COVID-19) with three compartments including susceptible, infected, and recovered class under Mittag-Leffler type derivative. The mentioned derivative has been introduced by Atangana, Baleanu, and Caputo abbreviated as (ABC) . Upon utilizing fixed point theory, we first prove the existence of at least one solution for the considered model and its uniqueness. Also, some results about stability of Ulam–Hyers type are also established. By applying a numerical technique called fractional Adams–Bashforth (AB) method, we develop a scheme for the approximate solutions to the considered model. Using some real available data, we perform the concerned numerical simulation corresponding to different values of fractional order. [ABSTRACT FROM AUTHOR]

Some fundamental conditions and hypotheses are established to ensure the existence, uniqueness, and stability to a class of implicit boundary value problems (BVPs) with Atangana–Baleanu–Caputo type derivative and integral. The required results are established by utilizing the Banach contraction mapping principle and fixed point theorem of Krasnoselskii. In addition, various types of stability results including Hyers–Ulam, generalized Hyers–Ulam, Hyers–Ulam–Rassias, and generalized Hyers–Ulam–Rassias stability are formulated for the problem under consideration. Pertinent examples are given to justify the results we obtain. [ABSTRACT FROM AUTHOR]

In this study, we develop a nonlinear ordinary differential equation to study the dynamics of syphilis transmission incorporating controls, namely prevention and treatment of the infected males and females. We obtain syphilis-free equilibrium (SFE) and syphilis-present equilibrium (SPE). We obtain the basic reproduction number, which can be used to control the transmission of the disease, and thus establish the conditions for local and global stability of the syphilis-free equilibrium. The stability results show that the model is locally asymptotically stable if the Routh–Hurwitz criteria are satisfied and globally asymptotically stable. The bifurcation analysis result reveals that the model exhibits backward bifurcation. We adopted Pontryagin's maximum principle to determine the optimality system for the syphilis model, which was solved numerically to show that syphilis transmission can be optimally best control using a combination of condoms usage and treatment in the primary stage of infection in both infected male and female populations. [ABSTRACT FROM AUTHOR]

Temperature is one of the integral environmental drivers that strongly affect the distribution and density of tsetse fly population. Precisely, ectotherm performance measures, such as development rate, survival probability and reproductive rate, increase from low values (even zero) at critical minimum temperature, peak at an optimum temperature and then decline to low levels (even zero) at a critical maximum temperature. In this study, a fractional-order Trypanosoma brucei rhodesiense model incorporating vector saturation and temperature dependent parameters is considered. The proposed model incorporates the interplay between vectors and two hosts, humans and animals. We computed the basic reproduction number and established results on the threshold dynamics. Meanwhile, we explored the effects of vector control and screening of infected host on long-term disease dynamics. We determine threshold levels essential to reducing the basic reproduction number to level below unity at various temperature levels. Our findings indicate that vector control and host screening could significantly control spread of the disease at different temperature levels. [ABSTRACT FROM AUTHOR]

In this manuscript, the fractional Atangana–Baleanu–Caputo model of prey and predator is studied theoretically and numerically. The existence and Ulam–Hyers stability results are obtained by applying fixed point theory and nonlinear analysis. The approximation solutions for the considered model are discussed via the fractional Adams Bashforth method. Moreover, the behavior of the solution to the given model is explained by graphical representations through the numerical simulations. The obtained results play an important role in developing the theory of fractional analytical dynamic of many biological systems. [ABSTRACT FROM AUTHOR]