Weighted Cauchy problem: fractional versus integer order

IF 0.9 4区数学 Q2 MATHEMATICS

Journal of Integral Equations and Applications Pub Date : 2021-12-01 DOI:10.1216/jie.2021.33.497

M. G. Morales, Z. Došlá

引用次数: 0

Abstract

This work is devoted to the solvability of the weighted Cauchy problem for fractional differential equations of arbitrary order, considering the Riemann-Liouville derivative. We show the equivalence between the weighted Cauchy problem and the Volterra integral equation in the space of Lebesgue integrable functions. Finally, we point out some discrepancies between the solutions for fractional and integer order case.

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加权柯西问题：分数阶与整数阶

本文研究了考虑Riemann-Liouville导数的任意阶分数阶微分方程的加权Cauchy问题的可解性。在Lebesgue可积函数空间中，给出了加权Cauchy问题与Volterra积分方程的等价性。最后指出了分数阶解与整数阶解之间的一些差异。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Integral Equations and Applications MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Integral Equations and Applications is an international journal devoted to research in the general area of integral equations and their applications. The Journal of Integral Equations and Applications, founded in 1988, endeavors to publish significant research papers and substantial expository/survey papers in theory, numerical analysis, and applications of various areas of integral equations, and to influence and shape developments in this field. The Editors aim at maintaining a balanced coverage between theory and applications, between existence theory and constructive approximation, and between topological/operator-theoretic methods and classical methods in all types of integral equations. The journal is expected to be an excellent source of current information in this area for mathematicians, numerical analysts, engineers, physicists, biologists and other users of integral equations in the applied mathematical sciences.