Research ArticleOpen AccessGoogle Scholar indexed
Iterative Technology in a Singular Fractional Boundary Value Problem with <i> q </i> -Difference
School of Mathematical Sciences, Qufu Normal University, Qufu, China
School of Mathematical Sciences, Qufu Normal University, Qufu, China
School of Mathematical Sciences, Qufu Normal University, Qufu, China
- 1 School of Mathematical Sciences, Qufu Normal University, Qufu, China
- 2 School of Mathematical Sciences, Qufu Normal University, Qufu, China
- 3 School of Mathematical Sciences, Qufu Normal University, Qufu, China
Copy link · social · email
Abstract
In this paper, we apply the iterative technology to establish the existence of solutions for a fractional boundary value problem with q -difference. Explicit iterative sequences are given to approxinate the solutions and the error estimations are also given.
KeywordsFractional Boundary Value Problem with q-DifferenceIterative SequenceGreen’s FunctionError Estimation
- Ferreira, R.A.C. (2011) Positive Solutions for a Class of Boundary Value Problems with Fractional q-Differences. Computers and Mathematics with Applications, 61, 367-373. http://dx.doi.org/10.1016/j.camwa.2010.11.012
- Li, X., Han, Z. and Li, X. (2015) Boundary Value Problems of Fractional q-Difference Schröinger Equations. Applied Mathematics Letters, 46, 100-105. http://dx.doi.org/10.1016/j.aml.2015.02.013
- Ferreira, R. (2011) Positive Solutions for a Class of Boundary Value Problems with Fractional q-Differences. Computers & Mathematics with Applications, 61, 367-373. http://dx.doi.org/10.1016/j.camwa.2010.11.012
- Li, X., Han, Z. and Sun, S. (2013) Existence of Positive Solutions of Nonlinear Fractional q-Difference Equation with Parameter. Advances in Difference Equations, 2013, 260. http://dx.doi.org/10.1186/1687-1847-2013-260
- Al-Salam, W.A. (1966-1967) Some Fractional q-Integrals and q-Derivatives. Proceedings of the Edinburgh Mathematical Society, 15, 135-140. http://dx.doi.org/10.1017/S0013091500011469
- Agarwal, R.P. (1969) Certain Fractional q-Integrals and q-Derivatives. Proceedings of the Cambridge Philosophical Society, 66, 365-370. http://dx.doi.org/10.1017/S0305004100045060
- Rajkovic, P.M., Marinkovic, S.D. and Stankovic, M.S. (2007) Fractional Integrals and Derivatives in q-Calculus. Applicable Analysis and Discrete Mathematics, 1, 311-323. http://dx.doi.org/10.2298/AADM0701311R
- Jankowski, T. (2014) Boundary Problems for Fractional Differential Equations. Applied Mathematics Letters, 28, 14-19. http://dx.doi.org/10.1016/j.aml.2013.09.004
- Mao, J., Zhao, Z. and Xu, N. (2010) On Existence and Uniqueness of Positive Solutions for Integral Boundary Boundary Value Problems. Electronic Journal of Qualitative Theory of Differential Equations, 16, 1-8. http://dx.doi.org/10.14232/ejqtde.2010.1.16
- Guo, D.J. and Lakshmikantham, V. (1988) Nonlinear Problems in Abstract Cones. Academic Press, Boston.
- Zhang, X., Liu, L. and Wu, Y. (2012) The Eigenvalue Problem for a Singular Higher Order Fractional Differential Equation Involving Fractional Derivatives. Applied Mathematics and Computation, 218, 8526-8536. http://dx.doi.org/10.1016/j.amc.2012.02.014
- Liu, Y., Zhang, W. and Liu, X. (2012) A Sufficient Condition for the Existence of a Positive Solution for a Nonlinear Fractional Differential Equation with the Riemann-Liouville Derivative. Applied Mathematics Letters, 25, 1986-1992. http://dx.doi.org/10.1016/j.aml.2012.03.018