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Nonlocal problems for Langevin-type differential equations with two fractional-order derivatives.
- Source :
- Boundary Value Problems; 2/24/2016, Vol. 2016 Issue 1, p1-21, 21p
- Publication Year :
- 2016
-
Abstract
- In this paper, we intend to study nonlocal problems for Langevin-type differential equations with two fractional derivatives of orders $\alpha,\beta\in(1,2)$. By using Laplace transform methods, formula of solutions involving Mittag-Leffler functions $A_{\alpha,\beta}(w)$, $\alpha,\beta\in(1,2)$, $w\in R$, and nonlocal terms of such equations are presented by studying the corresponding linear Langevin-type equations with two fractional derivatives. Meanwhile, existence results of solutions are established by utilizing boundedness, continuity, monotonicity, nonnegative of Mittag-Leffler function $A_{\alpha,\beta}(w)$, $\alpha,\beta\in(1,2)$, $w\in R$, and fixed point methods. Finally, two examples are presented to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16872762
- Volume :
- 2016
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Boundary Value Problems
- Publication Type :
- Academic Journal
- Accession number :
- 113272260
- Full Text :
- https://doi.org/10.1186/s13661-016-0560-4