{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T16:30:21Z","timestamp":1778949021171,"version":"3.51.4"},"reference-count":35,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,10,1]],"date-time":"2022-10-01T00:00:00Z","timestamp":1664582400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia","award":["GRANT492"],"award-info":[{"award-number":["GRANT492"]}]},{"name":"Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia","award":["AN000441"],"award-info":[{"award-number":["AN000441"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper we consider a fractional nonlinearity for the wave equation with friction and viscoelastic damping. Using Fixed point theorem a global in time existence of small data solutions to the Cauchy problem is investigated in this research. Our main interest is to show the influence of the fractional nonlinearity parameter to the admissible range of exponent \u03c2 comparing with power nonlinearity and also the generating of loss of decay.<\/jats:p>","DOI":"10.3390\/axioms11100524","type":"journal-article","created":{"date-parts":[[2022,10,8]],"date-time":"2022-10-08T00:07:43Z","timestamp":1665187663000},"page":"524","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Fractional Nonlinearity for the Wave Equation with Friction and Viscoelastic Damping"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0413-5626","authenticated-orcid":false,"given":"Abdelhamid","family":"Mohammed Djaouti","sequence":"first","affiliation":[{"name":"Preparatory Year Deanship, King Faisal University, Hofuf 31982, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2349-3445","authenticated-orcid":false,"given":"Muhammad Amer","family":"Latif","sequence":"additional","affiliation":[{"name":"Preparatory Year Deanship, King Faisal University, Hofuf 31982, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,1]]},"reference":[{"key":"ref_1","first-page":"73","article-title":"A new definition of fractional derivative without singular kernel","volume":"1","author":"Caputo","year":"2015","journal-title":"Prog. 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