This paper proposes a series-representations for the solution of initial value problems of linear inhomogeneous fractional differential equation with continuous variable coefficients. It is proved that the solution of the problem is determined by adding the solution of the inhomogeneous differential equations with the homogeneous initial conditions to the linear combination of the canonical fundamental system of solution for corresponding homogeneous fractional differential equation and the inhomogeneous initial values. The effectiveness of the theoretical analysis is illustrated with two examples.

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In this paper, we consider the following two-point boundary value problems of fuzzy linear fractional differential equations: (Dc1,1αy)(t)⊕b(t)⊗(Dc1,1βy)(t)⊕c(t)⊗y(t)=f(t), t∈(0,1), y(0)=y0 and y(1)=y1, where b,c∈C(I), b(t),c(t)≥0, y,f∈C(I,RF), I=[0,1], y0,y1∈RF and 1<β<α≤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.

In this paper, we investigate the necessary and sufficient conditions for existence of solutions for initial value problem of fuzzy Bagley-Torvik equation and the solution representation by using the multivariate Mittag-Leffler function. First we convert fuzzy initial value problem into the cut problem (system of fractional differential equations with inequality constraints) and obtain existence results for the solution of the cut problem under (1,1)- differentiability. Next we study the conditions for the solutions of the cut problem to constitute the solution of a fuzzy initial value problem and suggest a necessary and sufficient condition for the (1,1)-solution. Also, some examples are given to verify the effectiveness of our proposed method. The necessary and sufficient condition, solution representation for (1,2)-solution of initial value problem of fuzzy fractional Bagley-Torvik equation are shown in Appendix.

Ontology has become a fundamental and critical component for developing different applications on the Web. With the phenomenal growth of the Web resources, to generate automatically ontologies by using existing documents on the Web has gotten more and more attention. Forensic medicine ontology is used to narrate and reason the knowledge of a forensic domain. Previous studies for constructing forensic medicine ontologies have not automatically constructed by using all the semantic features of the Web documents. Hereby, it is difficult to rapidly construct an instance and property elements of ontology from the Web documents that are increasing daily. This paper focuses on the ontology generation method from forensic inquest documents structured on the Web. In order to generate most ontology elements for reasoning, we discuss how to generate hierarchical relationships, non-hierarchical relationships, and property elements based on structural and semantic characteristics of forensic inquest report. An empirical investigation of our method has proved the effectiveness of forensic medicine ontology generation. Experimental results show that our ontology generation method can generate with high quality rapidly and correctly important instances and properties of a forensic domain.