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Constructive existence of (1,1)-solutions to two-point value problems for fuzzy linear multiterm fractional differential equations. (English) Zbl 1474.34021

Summary: In this paper, we consider the following two-point boundary value problems of fuzzy linear fractional differential equations: \(({}^cD_{1,1}^\alpha y)(t) \oplus b(t) \otimes({}^cD_{1,1}^\beta y)(t) \oplus c(t) \otimes y(t) = f(t)\), \(t \in(0,1)\), \(y(0) = y_0\) and \(y(1) = y_1\), where \(b, c \in C(I)\), \(b(t), c(t) \geq 0\), \(y, f \in C(I, \mathbf{R}_{\mathrm{F}})\), \(I = [0,1]\), \(y_0, y_1 \in \mathbf{R}_{\mathrm{F}}\) and \(1 < \beta < \alpha \leq 2\). Our existence result is based on Banach fixed point theorem and the approximate solution of our problem is obtained by applying the Haar wavelet operational matrix.

MSC:

34A08 Fractional ordinary differential equations
34A07 Fuzzy ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
65L10 Numerical solution of boundary value problems involving ordinary differential equations
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