Introduction

Fractional operators find their applications in several scientific and engineering processes. We consider a fractional guava fruit model involving a non-local additionally non-singular fractional derivative for the interaction into guava pests and natural enemies. The fractional guava fruit model is considered as a Lotka-Volterra nature.

Objectives

The main objective of this work is to study a guava fruit model associated with a non-local additionally non-singular fractional derivative for the interaction into guava pests and natural enemies.

Methods

Existence and uniqueness analysis of the solution is evaluated effectively by using Picard Lindelof approach. An approximate numerical solution of the fractional guava fruit problem is obtained via a numerical scheme.

Results

The positivity analysis and equilibrium analysis for the fractional guava fruit model is discussed. The numerical results are demonstrated to prove our theoretical results. The graphical behavior of solution of the fractional guava problem at the distinct fractional order values and at various parameters is discussed.

Conclusion

The graphical behavior of solution of the fractional guava problem at the distinct fractional order values and at various parameters shows new vista and interesting phenomena of the model. The results are indicating that the fractional approach with non-singular kernel plays an important role in the study of different scientific problems. The suggested numerical scheme is very efficient for solving nonlinear fractional models of physical importance.

中文翻译：

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具有记忆效应的生物害虫防治番石榴分数模型分析

介绍

分数运算符在多个科学和工程过程中得到了应用。我们考虑了一个分数番石榴果实模型，该模型涉及一个非局部额外的非奇异分数导数，用于与番石榴害虫和天敌的相互作用。分数番石榴果实模型被认为是 Lotka-Volterra 性质。

目标

这项工作的主要目的是研究与非局部额外非奇异分数导数相关的番石榴果实模型，用于与番石榴害虫和天敌的相互作用。

方法

使用 Picard Lindelof 方法有效地评估解的存在性和唯一性分析。通过数值方案获得了分数番石榴果实问题的近似数值解。

结果

讨论了部分番石榴果实模型的正性分析和平衡分析。数值结果证明了我们的理论结果。讨论了在不同分数阶值和不同参数下分数番石榴问题的解的图形行为。

结论

在不同分数阶值和不同参数下分数番石榴问题的解的图形行为显示了模型的新前景和有趣的现象。结果表明，具有非奇异核的分数方法在不同科学问题的研究中发挥着重要作用。建议的数值方案对于求解具有物理重要性的非线性分数模型非常有效。