逐次逼近法在分数阶 $q$-微分方程初值问题中的应用

Abstract

Abstract:

This paper employs the method of successive approximations to investigate the existence of solutions for a class of initial value problems of fractional $q$-difference equations, as well as the existence of solutions for their corresponding systems. Subsequently, it presents approximate solutions for two specific types of fractional $q$-difference initial value problems (the fractional $q$-difference pantograph equation and the fractional $q$-difference Ambartsumian equation) along with their associated systems. Special emphasis is placed on discussing and analyzing several key properties of the approximate solutions for these two special equations.

Key words: initial value problem, fractional $q$-differential, continuous approximation method, approximate solutions

CLC Number:

O175.1

Caixia Guo, Jianmin Guo, Shugui Kang, Huapeng Li. The Successive Approximation Method for the Initial Value Problem of $q$-fractional Differential Equations[J].Acta mathematica scientia,Series A, 2026, 46(5): 1900-1931.

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The Successive Approximation Method for the Initial Value Problem of $q$-fractional Differential Equations

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