Uniform persistence and almost periodic solutions of a nonautonomous patch occupancy model

Abstract

In this paper, a nonlinear nonautonomous model in a rocky intertidal community is studied. The model is composed of two species in a rocky intertidal community and describes a patch occupancy with global dispersal of propagules and occupy each other by individual organisms. Firstly, we study the uniform persistence of the model via differential inequality techniques. Furthermore, a sharp threshold of global asymptotic stability and the existence of a unique almost periodic solution are derived. To prove the main results, we construct an appropriate Lyapunov function whose conditions are easily verified. The assumptions of the model are reasonable, and the results complement previously known ones. An example with specific values of parameters is included for demonstration of theoretical outcomes.

Numerical study of fractional order COVID-19 pandemic transmission model in context of ABO blood group

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Two sequential fractional hybrid differential inclusions

“…The fractional operators were developed over the years, and their importance has become more and more apparent to researchers today. Instances of the application of such fractional operators can be found in various sciences such as biomathematics, electrical circuits, medicine, and so on [1][2][3][4][5][6]. All these items have led researchers to find many aspects of the structure of the fractional boundary value problems and hereditary properties of their solutions.…”

Existence of solutions for nonlinear fractional integro-differential equations

“…Fractional differential equations have attracted much attention and have been the focus of many studies due mainly to their varied applications in many fields of science and engineering. In other words, fractional differential equations are widely used to describe many important phenomena in various fields such as physics, biophysics, chemistry, biology, control theory, economy and so on; see [14,19,23,29,33]. For an extensive literature in the study of fractional differential equations, we refer the reader to [2,11,15,16,18,20,21,24,26,30,32].…”