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The results involve the exponential integral function, convergent improper integrals on the infinite interval [Formula: see text] and the numerical integral method for the convolution integral. For both equations, stress responses to harmonic deformation display hysteresis phenomena and energy dissipation. The two constitutive equations characterize viscoelastic models of fluid-like and solid-like, respectively. <\/jats:p>","DOI":"10.1142\/s1793962317500404","type":"journal-article","created":{"date-parts":[[2017,3,21]],"date-time":"2017-03-21T22:21:09Z","timestamp":1490134869000},"page":"1750040","source":"Crossref","is-referenced-by-count":7,"title":["Mechanical response and simulation for constitutive equations with distributed order derivatives"],"prefix":"10.1142","volume":"08","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0986-1128","authenticated-orcid":false,"given":"Jun-Sheng","family":"Duan","sequence":"first","affiliation":[{"name":"School of Sciences, Shanghai Institute of Technology, 100 Haiquan Road, Fengxian District, Shanghai 201418, P. R. 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