# Generalized Monotone Iterative Techniques for Caputo Fractional IVP with an Application to Biological Models

## Abstract

We will begin this presentation with the definition and important properties of the Caputo fractional derivative. Next, we describe the main problem and define two different sets of coupled lower and upper solutions of a Caputo fractional differential equation with initial condition of order q, 0 < q < 1. The forcing function is the sum of an increasing function and a decreasing, which is common in classical applications such as the logistic model. Then, we develop two monotone iterative techniques, one corresponding to each set of lower and up- per solutions, which consist of sequences that converge uniformly and monotonically to minimal and maximal solutions of the IVP. Finally, we present an application example that illustrates our results.

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Generalized Monotone Iterative Techniques for Caputo Fractional IVP with an Application to Biological Models

We will begin this presentation with the definition and important properties of the Caputo fractional derivative. Next, we describe the main problem and define two different sets of coupled lower and upper solutions of a Caputo fractional differential equation with initial condition of order q, 0 < q < 1. The forcing function is the sum of an increasing function and a decreasing, which is common in classical applications such as the logistic model. Then, we develop two monotone iterative techniques, one corresponding to each set of lower and up- per solutions, which consist of sequences that converge uniformly and monotonically to minimal and maximal solutions of the IVP. Finally, we present an application example that illustrates our results.