{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T07:54:55Z","timestamp":1781250895218,"version":"3.54.1"},"reference-count":30,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,16]],"date-time":"2022-11-16T00:00:00Z","timestamp":1668556800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>As technology advances and the Internet makes our world a global village, it is important to understand the prospective career of freelancing. A novel symmetric fractional mathematical model is introduced in this study to describe the competitive market of freelancing and the significance of information in its acceptance. In this study, fixed point theory is applied to analyze the uniqueness and existence of the fractional freelance model. Its numerical solution is derived using the fractional Euler\u2019s method, and each case has been presented graphically as well as tabular. Further, the results have been compared with the classic freelance model and real data to show the importance of this model.<\/jats:p>","DOI":"10.3390\/sym14112424","type":"journal-article","created":{"date-parts":[[2022,11,16]],"date-time":"2022-11-16T02:31:27Z","timestamp":1668565887000},"page":"2424","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Freelance Model with Atangana\u2013Baleanu Caputo Fractional Derivative"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4766-028X","authenticated-orcid":false,"given":"Fareeha Sami","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Federal Urdu University of Arts, Science & Technology, Karachi 75300, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5233-6505","authenticated-orcid":false,"given":"M.","family":"Khalid","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Federal Urdu University of Arts, Science & Technology, Karachi 75300, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Areej A.","family":"Al-moneef","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2959-4212","authenticated-orcid":false,"given":"Ali Hasan","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq"},{"name":"Institute of Mathematics, University of Debrecen, Pf. 400, H-4002 Debrecen, Hungary"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7251-9608","authenticated-orcid":false,"given":"Omar","family":"Bazighifan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Hadhramout University, Hadhramout 50512, Yemen"},{"name":"Department of Mathematics, Faculty of Education, Seiyun University, Hadhramout 50512, Yemen"},{"name":"Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1113","DOI":"10.7498\/aps.54.1113","article-title":"The anomalous diffusion and fractional convection diffusion equation","volume":"54","author":"Chang","year":"2005","journal-title":"Acta Phys. 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