The Existence of Solutions for a Nonlinear First-Order Differential Equation Involving the Riemann–Liouville Fractional-Order and Nonlocal Condition
In this paper, we study necessary conditions for the existence and uniqueness of continuous solution for a nonlocal boundary value problem with nonlinear term involving Riemann–Liouville fractional derivative. Our results are based on Schauder fixed point theorem and the Banach contraction principle fixed point theorem. Examples illustrating the obtained results are also presented.
KeywordsFirst-order differential equation Riemann–Liouville fractional derivative Boundary value problem Existence of solutions Nonlocal condition
Mathematics Subject Classification26A33 34B10
The author wishes to express here thanks to the editor and the reviewers for a careful reading of this paper and the valuable comments and suggestions that led to the improvement of the original manuscript.
- 12.El-Sayed, A.M.A., Bin-Taher, E.O.: Positive solutions for a nonlocal multi-point bounday-value problem of fractional and second order. Electron. J. Differ. Equ. 2013(64), 1–8 (2014)Google Scholar
- 14.El-Sayed, A.M.A., Bin-Taher, E.O.: A nonlocal problem of an arbitrary (fractional) orders differential equation. Alex. J. Math. 1(2) (2010)Google Scholar
- 20.Hu, M., Wang, L.: Existence of solutions for a nonlinear fractional differential equation with integral boundary condition. Int. J. Math. Comput. Sci. 5(1), (2011)Google Scholar
- 22.Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and applications of fractional differential equations. In: van Mill, J. (ed.) North-Holland Mathematics Studies, vol. 204. Elsevier, Amsterdam (2006)Google Scholar
- 24.Murad, S.A., Hadid, S.: An existence and uniqueness theorem for fractional differential equation with integral boundary condition. J. Fract. Calc. Appl. 3(6), 1–9 (2012)Google Scholar
- 28.Zhang, M., Liu, Y.: Existence of solutions for implicit fractional differential systems with coupled nonlocal conditions. Adv. Anal. 2(1) (2017). https://doi.org/10.22606/aan.2017.11001