Estimation of unknown function of a class of integral inequalities and applications in fractional integral equations

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• 作者：Wu-Sheng Wang ; ^{wang4896@126.com" class="auth_mail" title="E-mail the corresponding author} ; ^{wang4896@sina.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Gronwall-type inequality ; Analysis technique ; Explicit bound ; Fractional integral equation
• 刊名：Applied Mathematics and Computation
• 出版年：2015
• 出版时间：1 October 2015
• 年：2015
• 卷：268
• 期：Complete
• 页码：1029-1037
• 全文大小：302 K

文摘

In this paper, we establish a class of iterated integral inequalities, which includes a nonconstant term outside the integrals. The upper bound of the embedded unknown function is estimated explicitly by adopting novel analysis techniques, such as: change of variable, amplification method, differential and integration. The derived result can be applied in the study of qualitative properties of solutions of fractional integral equations.