Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (6): 1334-1341.

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Existence of Mild Solutions for a Class of Fractional Semilinear Integro-Differential Equation of Mixed Type

Bo Zhu1,*(),Baoyan Han2,Lishan Liu3   

  1. 1 School of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014
    2 Common Course Teaching Department, Shandong University of Art and Design, Jinan 250014
    3 School of Mathematical Sciences, Qufu Normal University, Shandong Qufu 273165
  • Received:2018-08-29 Online:2019-12-26 Published:2019-12-28
  • Contact: Bo Zhu E-mail:zhubo207@163.com
  • Supported by:
    the PSDPHESTP(J16LI14);the NSFC(11871302)

Abstract:

In this paper, the authors studied the existence results of the mild solutions for a class of fractional semilinear integro-differential equation of mixed type by using the measure of noncompactness, k-set contraction and β-resolvent family. It is well known that the k-set contraction requires additional condition to ensure the contraction coefficient 0 < k < 1. We don't require additional condition to ensure the contraction coefficient 0 < k < 1. An example is introduced to illustrate the main results of this paper.

Key words: Fractional semilinear integro-differential equation of mixed type, k-Set contraction, Measure of noncompactness, β-Resolvent family

CLC Number: 

  • O175
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