Abstract
A new method is proposed for solving systems of fuzzy fractional differential equations (SFFDEs) with fuzzy initial conditions involving fuzzy Caputo differentiability. For this purpose, three cases are introduced based on the eigenvalue-eigenvector approach; then it is shown that the solution of system of fuzzy fractional differential equations is vector of fuzzy-valued functions. Then the method is validated by solving several examples.
Highlights
A lot of research has been focused on the application of fractional calculus, and such application is in the modelling of many physical and chemical processes as well as in engineering [1,2,3,4,5]
The nonlinear oscillation of earthquake can be modeled with fractional derivatives [6]
The analytic results on the existence and uniqueness of solutions to the fractional differential equations have been studied by many authors [19, 20]
Summary
A lot of research has been focused on the application of fractional calculus, and such application is in the modelling of many physical and chemical processes as well as in engineering [1,2,3,4,5]. Agarwal et al [34] proposed the concept of solutions for fractional differential equations with uncertainty which was followed by the authors in [35, 36] They have considered Riemann-Liouville’s differentiability to solve FFDEs which is a combination of the Hukuhara difference and the Riemann-Liouville derivative. Mathematical Problems in Engineering solutions of most of the FFDEs cannot be found ; in the recent years, attempts have been made to address this problem [39,40,41] It is with this motivation that we introduce in this paper an eigenvalue-eigenvector method for solving fuzzy fractional differential equations (FFDEs).
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