{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:41:04Z","timestamp":1760190064198,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,6,20]],"date-time":"2019-06-20T00:00:00Z","timestamp":1560988800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Different results regarding different integro-differentials are usually not properly generalized, as they often do not satisfy some of the constraints. The field of fuzzy integro-differentials is very rich these days because of their different applications and functions in different physical phenomena. Solutions of linear fuzzy Volterra integro-differential equations (FVIDEs) are more generalized and have better applications. In this report, the Sumudu decomposition method (SDM) was used to find the solution to some linear and nonlinear fuzzy integro-differential equations (FIDEs). Some examples are given to show the validity of the presented method.<\/jats:p>","DOI":"10.3390\/axioms8020074","type":"journal-article","created":{"date-parts":[[2019,6,20]],"date-time":"2019-06-20T10:49:59Z","timestamp":1561027799000},"page":"74","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Sumudu Decomposition Method for Solving Fuzzy Integro-Differential Equations"],"prefix":"10.3390","volume":"8","author":[{"given":"Shin Min","family":"Kang","sequence":"first","affiliation":[{"name":"Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University, Jinju 52828, Korea"},{"name":"Center for General Education, China Medical University, Taichung 40402, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zain","family":"Iqbal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Engineering and Technology, Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mustafa","family":"Habib","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Engineering and Technology, Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5488-0467","authenticated-orcid":false,"given":"Waqas","family":"Nazeer","sequence":"additional","affiliation":[{"name":"Division of Science and Technology, University of Education, Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,20]]},"reference":[{"key":"ref_1","unstructured":"Ullah, S., Farooq, M., Ahmad, L., and Abdullah, S. (2014). Application of fuzzy Laplace transforms for solving fuzzy partial Volterra integro-differential equations. arXiv."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Mikaeilv, N., Khakrangin, S., and Allahviranloo, T. (2011, January 18\u201322). Solving fuzzy Volterra integro-differential equation by fuzzy differential transform method. Proceedings of the 7th Conference of the European Society for Fuzzy Logic and Technology, Aix-Les-Bains, France.","DOI":"10.2991\/eusflat.2011.56"},{"key":"ref_3","first-page":"5","article-title":"Solution of Different Types of Fuzzy Integro-Differential Equations Via Laplace Homotopy Perturbation Method","volume":"17","author":"Ahmad","year":"2017","journal-title":"J. Sci. Arts"},{"key":"ref_4","unstructured":"Mohmmed, S.E.A.A. (2016). Solution of Linear and Nonlinear Partial Differential Equations by Mixing Adomian Decomposition Method and Sumudu Transform. [Ph.D. Thesis, Sudan University of Science and Technology]."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Eltayeb, H., and K\u0131l\u0131\u00e7man, A. (2012). Application of Sumudu decomposition method to solve nonlinear system of partial differential equations. Abstract and Applied Analysis, Hindawi.","DOI":"10.1155\/2012\/412948"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Gomes, L.T., de Barros, L.C., and Bede, B. (2015). Fuzzy Differential Equations in Various Approaches, Springer.","DOI":"10.1007\/978-3-319-22575-3"},{"key":"ref_7","first-page":"291","article-title":"Method for solving fuzzy integro-differential equations by using fuzzy Laplace transformation","volume":"3","author":"Das","year":"2014","journal-title":"Int. J. Sci. Tech."},{"key":"ref_8","first-page":"515","article-title":"Sumudu decomposition method for nonlinear equations","volume":"7","author":"Kumar","year":"2012","journal-title":"Int. Math. Forum"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"285","DOI":"10.18576\/msl\/050310","article-title":"The use of Sumudu decomposition method for solving predator-prey systems","volume":"5","author":"Bildik","year":"2016","journal-title":"Math. Sci. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1098\/rspa.1971.0097","article-title":"The application of integral equation methods to the numerical solution of some exterior boundary-value problems","volume":"323","author":"Burton","year":"1971","journal-title":"Proc. R. Soc. Lond. A Math. Phys. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Wazwaz, A.M. (2015). A First Course in Integral Equations, World Scientific Publishing Company.","DOI":"10.1142\/9570"},{"key":"ref_12","first-page":"107","article-title":"Fuzzy integro-differential equations: Discrete solution and error estimation","volume":"10","author":"Zeinali","year":"2013","journal-title":"Iran. J. Fuzzy Syst."},{"key":"ref_13","first-page":"3173","article-title":"Solving Fuzzy Linear Volterra Intergro-Differential Equation Using Fuzzy Sumudu Transform","volume":"119","author":"Rajkumar","year":"2018","journal-title":"Int. J. Pure Appl. Math."},{"key":"ref_14","first-page":"30","article-title":"A new iterative technique for a fractional model of nonlinear Zakharov\u2013Kuznetsov equations via Sumudu transform","volume":"334","author":"Prakash","year":"2018","journal-title":"Appl. Math. Comput."},{"key":"ref_15","first-page":"12","article-title":"An efficient numerical algorithm for the fractional Drinfeld\u2013Sokolov\u2013Wilson equation","volume":"335","author":"Singh","year":"2018","journal-title":"Appl. Math. Comput."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/j.jksus.2017.05.002","article-title":"Local fractional Sumudu decomposition method for linear partial differential equations with local fractional derivative","volume":"31","author":"Ziane","year":"2017","journal-title":"J. King Saud Univ. Sci."},{"key":"ref_17","first-page":"301","article-title":"Homotopy analysis Sumudu transform method for nonlinear equations","volume":"4","author":"Rathore","year":"2012","journal-title":"Int. J. Ind. Math."},{"key":"ref_18","unstructured":"Li, K., and Xie, Y. (2012, January 6\u20139). A brief introduction of Sumudu transform and comparison with other integral transforms. Proceedings of the 6th Asia-Pacific Conference on Environmental Electromagnetics (CEEM), Shanghai, China."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/8\/2\/74\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:59:56Z","timestamp":1760187596000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/8\/2\/74"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,20]]},"references-count":18,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,6]]}},"alternative-id":["axioms8020074"],"URL":"https:\/\/doi.org\/10.3390\/axioms8020074","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2019,6,20]]}}}