Abstract
In this paper, fuzzy nth-order derivative for n in N is introduced. To do this, nth-order derivation under generalized Hukuhara derivative here in discussed. Calculations on the fuzzy nth-order derivative on fuzzy functions and their relationships, in general, are introduced. Then, the fuzzy nth-order differential equations is solved, for n in N.
Highlights
The H-derivative of fuzzy number valued function was introduced by Siekalla in [22]
This derivation amplifies the fuzziness when time goes by [8], strongly general differentiability was introduced in this paper and have been studied by many researchers, this concept allows us to solve the problems of H-derivative
The fuzzy derivations are very important for solving fuzzy equations for instance, fuzzy differential equations and fuzzy integro-differential equations
Summary
The H-derivative of fuzzy number valued function was introduced by Siekalla in [22] This derivation amplifies the fuzziness when time goes by [8], strongly general differentiability was introduced in this paper and have been studied by many researchers, this concept allows us to solve the problems of H-derivative. Two cases of them are always very important and the two others are important to acquire switching point He used these four cases of derivatives for solving fuzzy differential equations. Allahviranloo and hooshangian introduced fuzzy generalized H-differential and used it to solve fuzzy differential equations of secondorder, [4]. An algorithm is introduced to find fuzzy nth-order derivation and its cases for all, in general. Fuzzy differential equations in general form are solved.
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