Author:
Hassan Habibu,Tahir Alhaji
Abstract
In this study, a third nonlinear fuzzy ordinary differential equation is defined and established in Hilbert space using extension principle. The results obtained gives clear distinction between this work and the existing ones in the literature an example is formulated which shows that a closed subset of a Hilbert space is a Hilbert Space. It is recommended that future study should consider the development of system of third order linear and nonlinear fuzzy ordinary differential equations in Hilbert space by the extension principle.
Publisher
Umaru Musa YarAdua University Katsina NG
Reference15 articles.
1. Abu Arqub, O., Al-Smadi, M., Momani, S., Hayat, T. (2016). Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method. Soft Comput. 20, 3283-3302. https://doi.org/10.1007/s00500-015-1707-4
2. Ahmadian, A., Salahshour, S., Chan, C.S., Baleanu, D. (2018). Numerical solutions of fuzzy differential equations by an efficient Runge-Kutta method with generalized differentiability. Fuzzy Sets Syst. 331, 47-67. https://doi.org/10.1016/j.fss.2016.11.013
3. Anke, K., Rainer P., Stefan, S., Sascha T. and Marcus, W. (2012). A Hilbert space perspective on ordinary differential equations with memory term. institut für analysis, fachrichtung mathematic technische universität Dresden Germany at: https://www.researchgate.net/publication/224014343
4. Buckley J. J. and Feuring, T. (2000). Fuzzy differential equations, Fuzzy Sets Syst., vol. 110, pp. 43-54. https://doi.org/10.1016/S0165-0114(98)00141-9
5. ElJaoui, E., Melliani, S. & Chadli, L. S. (2015). Solving second-order fuzzy differential equations by the fuzzy Laplace transform method, Springer journal of advances in difference equations. https://doi.org/10.1186/s13662-015-0414-x