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Fuzzy differential equation

From Wikipedia, the free encyclopedia

Fuzzy differential equation are general concept of ordinary differential equation in mathematics defined as differential inclusion for non-uniform upper hemicontinuity convex set with compactness in fuzzy set.[1][2][3] for all .

First order fuzzy differential equation

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A first order fuzzy differential equation[4] with real constant or variable coefficients

where is a real continuous function and is a fuzzy continuous function such that .

Linear systems of fuzzy differential equations

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A system of equations of the form

where are real functions and are fuzzy functions

Fuzzy partial differential equations

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A fuzzy differential equation with partial differential operator is for all .

Fuzzy fractional differential equation

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A fuzzy differential equation with fractional differential operator is

for all where is a rational number.

References

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  1. ^ "Theory of Fuzzy Differential Equations and Inclusions". Routledge & CRC Press. Retrieved 2022-10-15.
  2. ^ Devi, S. Sindu; Ganesan, K. (2019). "Application of linear fuzzy differential equation in day to day life". The 11th National Conference on Mathematical Techniques and Applications. Vol. 2112. Chennai, India. p. 020169. doi:10.1063/1.5112354. S2CID 198460805.{{cite book}}: CS1 maint: location missing publisher (link)
  3. ^ Qiu, Dong; Lu, Chongxia; Zhang, Wei; Zhang, Qinghua; Mu, Chunlai (2014-12-02). "Basic theorems for fuzzy differential equations in the quotient space of fuzzy numbers". Advances in Difference Equations. 2014 (1): 303. doi:10.1186/1687-1847-2014-303. ISSN 1687-1847. S2CID 54172371.
  4. ^ Keshavarz, M.; Allahviranloo, T.; Abbasbandy, S.; Modarressi, M. H. (2021). "A Study of Fuzzy Methods for Solving System of Fuzzy Differential Equations". New Mathematics and Natural Computation. 17: 1–27. doi:10.1142/s1793005721500010. S2CID 225373837. Retrieved 2022-10-15.