On the existence of solutions to periodic boundary value problems for fuzzy linear differential equations

2013 ◽  
Vol 219 ◽  
pp. 1-26 ◽  
Author(s):  
Rosana Rodríguez-López
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Periodic Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Linear Differential Equations ◽  
Periodic Boundary Value Problems ◽  
Linear Differential

A new method for converting boundary value problems for impulsive fractional differential equations to integral equations and its applications

2017 ◽  
Vol 8 (1) ◽  
pp. 386-454 ◽  
Author(s):  
Yuji Liu
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Periodic Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Impulsive Fractional Differential Equations ◽  
Periodic Boundary Value Problems ◽  
Fractional Differential

Abstract In this paper, we present a new method for converting boundary value problems of impulsive fractional differential equations to integral equations. Applications of this method are given to solve some types of anti-periodic boundary value problems for impulsive fractional differential equations. Firstly by using iterative method, we prove existence and uniqueness of solutions of Cauchy problems of differential equations involving Caputo fractional derivative, Riemann–Liouville and Hadamard fractional derivatives with order {q\in(0,1)} , see Theorem 2, Theorem 4, Theorem 6 and Theorem 8. Then we obtain exact expression of piecewise continuous solutions of these fractional differential equations see Theorem 1, Theorem 2, Theorem 3 and Theorem 4. Finally, four classes of integral type anti-periodic boundary value problems of singular fractional differential equations with impulse effects are proposed. Sufficient conditions are given for the existence of solutions of these problems. See Theorems 4.1–4.4. We allow the nonlinearity {p(t)f(t,x)} in fractional differential equations to be singular at {t=0,1} and be involved a super-linear and sub-linear term. The analysis relies on Schaefer’s fixed point theorem. In order to avoid misleading readers, we correct the results in [28] and [65]. We establish sufficient conditions for the existence of solutions of an anti-periodic boundary value problem for impulsive fractional differential equation. The results in [68] are complemented. The results in [81] are corrected. See Lemma 5.1, Lemma 5.7, Lemma 5.10 and Lemma 5.13.

Test for Disconjugacy of a Differential Inclusion of Neutral Type

1997 ◽  
Vol 4 (2) ◽  
pp. 101-108
Author(s):  
A. Haščák
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Differential Inclusion ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Neutral Type ◽  
Linear Differential Equations ◽  
Multipoint Boundary ◽  
Linear Differential ◽  
Multipoint Boundary Value Problems

Abstract Generalizations of the disconjugacy for a differential inclusion of neutral type are given. The relation between these generalizations and the existence of solutions of multipoint boundary value problems is discussed and the tests for disconjugacy are established. These tests are applicable to the linear differential equations of neutral type, too.

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