Mathematical Modelling of Natural Phenomena 

About: Mathematical Modelling of Natural Phenomena is an academic journal published by EDP Sciences. The journal publishes majorly in the area(s): Population & Nonlinear system. It has an ISSN identifier of 0973-5348. Over the lifetime, 1001 publications have been published receiving 13744 citations. The journal is also known as: MMNP (Online) & MMNP.

New numerical approach for fractional differential equations

Abstract: In the present case, we propose the correct version of the fractional Adams-Bashforth methods which take into account the nonlinearity of the kernels including the power law for the Riemann-Liouville type, the exponential decay law for the Caputo-Fabrizio case and the Mittag-Leffler law for the Atangana-Baleanu scenario.The Adams-Bashforth method for fractional differentiation suggested and are commonly use in the literature nowadays is not mathematically correct and the method was derived without taking into account the nonlinearity of the power law kernel. Unlike the proposed version found in the literature, our approximation, in all the cases, we are able to recover the standard case whenever the fractional power α = 1. Numerical results are finally given to justify the effectiveness of the proposed schemes.

Pattern and Waves for a Model in Population Dynamics with Nonlocal Consumption of Resources

Abstract: We study a reaction-diffusion equation with an integral term describing nonlocal consumption of resources in population dynamics. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. They can be related to the emergence of biological species due to the intra-specific competition and random mutations. Various types of travelling waves are observed.

Epidemiological Models and Lyapunov Functions

Abstract: We give a survey of results on global stability for deterministic compartmental epidemi- ological models Using Lyapunov techniques we revisit a classical result, and give a simple proof By the same methods we also give a new result on differential susceptibility and infectivity models with mass action and an arbitrary number of compartments These models encompass the so-called differential infectivity and staged progression models In the two cases we prove that if the basic reproduction ratio R0 • 1, then the disease free equilibrium is globally asymptotically stable If R0 > 1, there exists an unique endemic equilibrium which is asymptotically stable on the positive orthant

Inverse Stable Subordinators

Abstract: The inverse stable subordinator provides a probability model for time-fractional differential equations, and leads to explicit solution formulae. This paper reviews properties of the inverse stable subordinator, and applications to a variety of problems in mathematics and physics. Several different governing equations for the inverse stable subordinator have been proposed in the literature. This paper also shows how these equations can be reconciled.

Unbounded Laplacians on Graphs: Basic Spectral Properties and the Heat Equation

Abstract: We discuss Laplacians on graphs in a framework of regular Dirichlet forms. We focus on phenomena related to unboundedness of the Laplacians. This includes (failure of) essential selfadjointness, absence of essential spectrum and stochastic incompleteness.