Existence Results for Solutions of Nabla Fractional Boundary Value Problems with General Boundary Conditions

Öz

In this article, we consider a particular class of nabla fractional boundary value problems with general boundary conditions, 

and establish sufficient conditions on existence and uniqueness of its solutions.

Anahtar Kelimeler

• Nabla fractional difference,boundary value problem,fixed point,existence

Kaynakça

1. Abdeljawad, Thabet; Atıcı, Ferhan M. On the definitions of nabla fractional operators. Abstr. Appl. Anal. 2012, Art. ID 406757, 13 pp.
2. Agarwal, Ravi P.; Meehan, Maria; O’Regan, Donal, Fixed point theory and applications. Cambridge Tracts in Mathematics, 141. Cambridge University Press, Cambridge, 2001.
3. Ahrendt, K.; Castle, L.; Holm, M.; Yochman, K. Laplace transforms for the nabla-difference operator and a fractional variation of parameters formula. Commun. Appl. Anal. 16 (2012), no. 3, 317--347.
4. Areeba Ikram. Green's Functions and Lyapunov Inequalities for Nabla Caputo Boundary Value Problems. PhD thesis, University of Nebraska-Lincoln, 2018. Atıcı, Ferhan M.; Eloe, Paul W. Discrete fractional calculus with the nabla operator. Electron. J. Qual. Theory Differ. Equ. 2009, Special Edition I, No. 3, 12 pp.
5. Bohner, Martin; Peterson, Allan Dynamic equations on time scales. An introduction with applications. Birkh\"{a}user Boston, Inc., Boston, MA, 2001. x+358 pp.
6. Brackins, Abigail; Boundary value problems of nabla fractional difference equations. Thesis (Ph.D.)–The University of Nebraska - Lincoln. 2014. 92 pp.
7. Gholami, Yousef; Ghanbari, Kazem Coupled systems of fractional $\nabla$-difference boundary value problems. Differ. Equ. Appl. 8 (2016), no. 4, 459--470. Goodrich, Christopher; Peterson, Allan C. Discrete fractional calculus. Springer, Cham, 2015.
8. Ikram, Areeba; Lyapunov inequalities for nabla Caputo boundary value problems. J. Difference Equ. Appl. 25 (2019), no. 6, 757--775.

9. Jonnalagadda, Jagan Mohan An ordering on Green's function and a Lyapunov-type inequality for a family of nabla fractional boundary value problems. Fract. Differ. Calc. 9 (2019), no. 1, 109--124.
10. Jonnalagadda, Jaganmohan Analysis of a system of nonlinear fractional nabla difference equations. Int. J. Dyn. Syst. Differ. Equ. 5 (2015), no. 2, 149--174.
11. Jonnalagadda, Jaganmohan Discrete fractional Lyapunov-type inequalities in nabla sense. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. Manuscript submitted for publication.
12. Jonnalagadda, Jagan Mohan Lyapunov-type inequalities for discrete Riemann-Liouville fractional boundary value problems. Int. J. Difference Equ. 13 (2018), no. 2, 85--103.
13. Jonnalagadda, Jagan Mohan On two-point Riemann-Liouville type nabla fractional boundary value problems. Adv. Dyn. Syst. Appl. 13 (2018), no. 2, 141--166.
14. Jonnalagadda, Jagan Mohan On a nabla fractional boundary value problem with general boundary conditions. AIMS Mathematics. To appear.
15. Kelley, Walter G.; Peterson, Allan C. Difference equations. An introduction with applications. Second edition. Harcourt/Academic Press, San Diego, CA, 2001.
16. Kilbas, Anatoly A.; Srivastava, Hari M.; Trujillo, Juan J. Theory and applications of fractional differential equations. North-Holland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam, 2006.
17. Podlubny, Igor Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Mathematics in Science and Engineering, 198. Academic Press, Inc., San Diego, CA, 1999.