GENERALIZED MONOTONE METHOD FOR CAPUTO FRACTIONAL DIFFERENTIAL EQUATION WITH APPLICATIONS TO POPULATION MODELS

Monotone method combined with method of upper and lower solutions is a productive technique to prove existence of extremal solutions in dynamic systems. However, this method is applicable when the forcing function is increasing or can be made increasing by adding a linear term. Monotone method also...

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Bibliographic Details
Published in:Neural, parallel & scientific computations parallel & scientific computations, 2012-06, Vol.20 (2), p.119-132
Main Authors: Pham, Th T, Ramirez, J D, Vatsala, A S
Format: Article
Language:English
Subjects:
Combustion
Differential equations
Dynamical systems
Dynamics
Initial conditions
Logistics
Mathematical analysis
Mathematical models
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Summary:Monotone method combined with method of upper and lower solutions is a productive technique to prove existence of extremal solutions in dynamic systems. However, this method is applicable when the forcing function is increasing or can be made increasing by adding a linear term. Monotone method also works when the forcing function is decreasing in dynamic systems. In this work, we prove existence of coupled minimal and maximal solutions by using generalized monotone method for Caputo fractional differential equation with initial condition. Also, we consider the case when the forcing function is the sum of an increasing and decreasing function. In general, this is true for many mathematical models, including population models and chemical combustion models. Finally, we obtain numerical results to demonstrate an application of our theoretical results of the Logistic equation.
ISSN:1061-5369