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Next we study the conditions for the solutions of the cut problem to constitute the solution of a fuzzy initial value problem and suggest a necessary and sufficient condition for the (1,1)-solution. Also, some examples are given to verify the effectiveness of our proposed method. The necessary and sufficient condition, solution representation for (1,2)-solution of initial value problem of fuzzy fractional Bagley-Torvik equation are shown in Appendix.<\/jats:p>","DOI":"10.3233\/jifs-202453","type":"journal-article","created":{"date-parts":[[2021,6,15]],"date-time":"2021-06-15T13:54:10Z","timestamp":1623765250000},"page":"639-654","source":"Crossref","is-referenced-by-count":2,"title":["Necessary and sufficient conditions for existence of solutions for initial value problem of fuzzy Bagley-Torvik equation and solution representation"],"prefix":"10.1177","volume":"41","author":[{"given":"Sunae","family":"Pak","sequence":"first","affiliation":[{"name":"Faculty of Mathematics, Kim Il Sung University, Pyongyang, DPR Korea"}]},{"given":"Huichol","family":"Choe","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics, Kim Il Sung University, Pyongyang, DPR Korea"}]},{"given":"Kinam","family":"Sin","sequence":"additional","affiliation":[{"name":"Faculty 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