Purpose

The purpose of this paper is to obtain a numerical scheme for finding numerical solutions of linear and nonlinear fractional differential equations involving ψ-Caputo derivative.

Design/methodology/approach

An operational matrix to find numerical approximation of ψ-fractional differential equations (FDEs) is derived. This study extends the method to nonlinear FDEs by using quasi linearization technique to linearize the nonlinear problems.

Findings

The error analysis of the proposed method is discussed in-depth. Accuracy and efficiency of the method are verified through numerical examples.

Research limitations/implications

The method is simple and a good mathematical tool for finding solutions of nonlinear ψ-FDEs. The operational matrix approach offers less computational complexity.

Originality/value

Engineers and applied scientists may use the present method for solving fractional models appearing in applications.

中文翻译：

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数值求解分数阶微分方程的ψ-Haar小波方法

目的

本文的目的是获得一个数值方案，以寻找涉及ψ- Caputo导数的线性和非线性分数阶微分方程的数值解。

设计/方法/方法

运算矩阵找到的数值逼近ψ -fractional微分方程（泛函微分方程）导出。本研究通过使用准线性化技术将非线性问题线性化，将方法扩展到非线性FDE。

发现

对该方法的误差分析进行了深入探讨。通过数值算例验证了该方法的准确性和有效性。

研究局限/意义

该方法简单易行，是寻找非线性ψ- FDEs解的良好数学工具。运算矩阵方法提供较少的计算复杂性。

创意/价值

工程师和应用科学家可以使用本方法来求解应用程序中出现的分数模型。