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The objective of this research is to propose a fuzzy solution for a specific type of uncertain fractional descriptor linear systems referred to as granular fractional descriptor linear systems (gr-FFDLSs). The coefficients, boundary conditions, and parameters in gr-FFDLSs are represented as fuzzy numbers. This type of system also encompasses the concept of fractional order granular Caputo (gr-Caputo) fuzzy derivative. To achieve this goal, the gr-Caputo fuzzy derivative of order n - 1 < β < n , where n is a natural number, is defined. Furthermore, the granular fuzzy Laplace transforms of the fractional order gr-Caputo fuzzy derivative and fractional order granular fuzzy integrals are introduced. Using the definition of fractional order gr-Caputo fuzzy derivative, fuzzy Drazin inverse matrix, and Laplace transformation, the solution to the state equation of granular descriptor fuzzy fractional linear systems is obtained. Two techniques, the fuzzy shuffle algorithm and the fuzzy Drazin inverse method, are presented to find the fuzzy solution of gr-FFDLSs. To demonstrate the effectiveness of these techniques, two examples are provided to show that they can produce accurate solutions for gr-FFDLSs. [ABSTRACT FROM AUTHOR]

This paper aims to provide a fuzzy solution for fuzzy singular differential equations (FSDEs) in which the coefficient matrices and/or initial conditions are considered as fuzzy matrices and/or numbers. In addition, the fuzzy derivative is in the sense of the granular derivative. To achieve the aim, some new concepts such as the rank and index of fuzzy matrices, and granular inverse of a nonsingular fuzzy matrix are presented. Moreover, a fuzzy matrix called fuzzy Drazin inverse matrix is defined which has a pivotal role of a fuzzy inverse matrix of a singular fuzzy matrix. Furthermore, two approaches for finding the fuzzy Drazin inverse matrix are given. In order to present the solution of FSDEs, a definition of nth order granular derivative is presented. This paper closes with some examples showing the approach is capable of finding the solution of FSDEs. [ABSTRACT FROM AUTHOR]