Research Article

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

Volume: 4 Number: 1 March 31, 2020
EN

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

Abstract

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.

Keywords

References

  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.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

March 31, 2020

Submission Date

October 18, 2019

Acceptance Date

December 6, 2019

Published in Issue

Year 2020 Volume: 4 Number: 1

APA
Jonnalagadda, J. M. (2020). Existence Results for Solutions of Nabla Fractional Boundary Value Problems with General Boundary Conditions. Advances in the Theory of Nonlinear Analysis and Its Application, 4(1), 29-42. https://doi.org/10.31197/atnaa.634557
AMA
1.Jonnalagadda JM. Existence Results for Solutions of Nabla Fractional Boundary Value Problems with General Boundary Conditions. ATNAA. 2020;4(1):29-42. doi:10.31197/atnaa.634557
Chicago
Jonnalagadda, Jagan Mohan. 2020. “Existence Results for Solutions of Nabla Fractional Boundary Value Problems With General Boundary Conditions”. Advances in the Theory of Nonlinear Analysis and Its Application 4 (1): 29-42. https://doi.org/10.31197/atnaa.634557.
EndNote
Jonnalagadda JM (March 1, 2020) Existence Results for Solutions of Nabla Fractional Boundary Value Problems with General Boundary Conditions. Advances in the Theory of Nonlinear Analysis and its Application 4 1 29–42.
IEEE
[1]J. M. Jonnalagadda, “Existence Results for Solutions of Nabla Fractional Boundary Value Problems with General Boundary Conditions”, ATNAA, vol. 4, no. 1, pp. 29–42, Mar. 2020, doi: 10.31197/atnaa.634557.
ISNAD
Jonnalagadda, Jagan Mohan. “Existence Results for Solutions of Nabla Fractional Boundary Value Problems With General Boundary Conditions”. Advances in the Theory of Nonlinear Analysis and its Application 4/1 (March 1, 2020): 29-42. https://doi.org/10.31197/atnaa.634557.
JAMA
1.Jonnalagadda JM. Existence Results for Solutions of Nabla Fractional Boundary Value Problems with General Boundary Conditions. ATNAA. 2020;4:29–42.
MLA
Jonnalagadda, Jagan Mohan. “Existence Results for Solutions of Nabla Fractional Boundary Value Problems With General Boundary Conditions”. Advances in the Theory of Nonlinear Analysis and Its Application, vol. 4, no. 1, Mar. 2020, pp. 29-42, doi:10.31197/atnaa.634557.
Vancouver
1.Jagan Mohan Jonnalagadda. Existence Results for Solutions of Nabla Fractional Boundary Value Problems with General Boundary Conditions. ATNAA. 2020 Mar. 1;4(1):29-42. doi:10.31197/atnaa.634557

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