Hamidi, M., Nyamoradi, N. (2017). On boundary value problem for fractional differential equations. Bulletin of the Iranian Mathematical Society, 43(3), 789-805.

M.R. Hamidi; N. Nyamoradi. "On boundary value problem for fractional differential equations". Bulletin of the Iranian Mathematical Society, 43, 3, 2017, 789-805.

Hamidi, M., Nyamoradi, N. (2017). 'On boundary value problem for fractional differential equations', Bulletin of the Iranian Mathematical Society, 43(3), pp. 789-805.

Hamidi, M., Nyamoradi, N. On boundary value problem for fractional differential equations. Bulletin of the Iranian Mathematical Society, 2017; 43(3): 789-805.

On boundary value problem for fractional differential equations

^{1}Department of Mathematics, Faculty of Sciences, Razi University, 67149 Kermanshah, Iran.

^{2}Department of Mathematics, Faculty of Sciences, Razi University, 67149 Kermanshah, Iran.

Abstract

In this paper, we study the existence of solutions for a fractional boundary value problem. By using critical point theory and variational methods, we give some new criteria to guarantee that the problems have at least one solution and infinitely many solutions.

T. Bartsch, In_nitely many solutions of a symmetric Dirichlet problem, Nonlinear Anal. 20 (1993), no. 10, 1205--1216.

T. Bartsch and S.J. Li, Critical point theory for asymptotically quadratic functional and applications to problems with resonance, Nonlinear Anal. 28 (1997), no. 3, 419--441.

G. Bonanno, R. Rodriguez-Lopez and S. Tersian, Existence of solutions to boundary value problem for impulsive fractional differential equations, Fract. Calc. Appl. Anal. 17 (2014), no. 3, 717--744.

F. Jiao and Y. Zhou, Existence of solutions for a class of fractional boundary value problems via critical point theory, Comput. Math. Appl. 62 (2011), no. 3, 1181--1199.

F. Jiao and Y. Zhou, Existence results for fractional boundary value problem via critical point theory, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 22 (2012), no. 4, 1--17.

A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies 204, Elsevier Science, Amsterdam, 2006.

A.A. Kilbas and J.J. Trujillo, Differential equations of fractional order: methods, results and problems I, Appl. Anal. 78 (2001), no. 1-2, 153--192.

A.A. Kilbas and J.J. Trujillo, Differential equations of fractional order: methods, results and problems II, Appl. Anal. 81 (2002), no. 2, 435--493.

Y.N. Li, H.R. Sun and Q.G. Zhang, Existence of solutions to fractional boundary-value problems with a parameter, Electron. J. Differential Equations 2013 (2013), no. 141, 12 pages.

J. Nieto and D. O'Regan, Variational approach to impulsive differential equations, Non-linear Anal. Real World Appl. 10 (2009), no. 2, 680--690.

I. Podlubny, Fractional Differential Equations, Academic Press, NewYork, 1999.

R. Rodriguez- Lopez and S. Tersian, Multiple solutions to boundary value problem for impulsive fractional differential equations, Fract. Calc. Appl. Anal. 17 (2014), no. 4, 1016--1038.

C. Torres, Existence of solutions for fractional Hamiltonian systems, Electron. J. Differential Equations 2013 (2013), no 259, 12 pages.

M. Willem, Minimax Theorems, Birkhäuser, Boston, 1996.

Z.Q. Wang, On a superlinear elliptic equation, Ann. Inst. H. Poincare Anal. Non Lineaire 8 (1991), no. 1, 43--57.