рус eng
«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2025. Vol 51

Positive Solutions of Nabla Fractional Sturm–Liouville Problems

Author(s)
Jagan Mohan Jonnalagadda1, Juan E. Napoles Valdes2,3

1Birla Institute of Technology and Science, Pilani, Hyderabad, Telangana, India

2National University of the Northeast, Corrientes, Argentina

3National Technological University, Resistencia, Argentina

Abstract
This article discusses the existence of positive solutions to Sturm–Liouville boundary value problems for Riemann–Liouville nabla fractional difference equations. The results obtained here shall generalize the existing ones. We provide a few examples to illustrate the applicability of established results.
About the Authors

Jagan Mohan Jonnalagadda, PhD (Math.), Assoc. Prof., Birla Institute of Technology and Science, Pilani, Hyderabad, Telangana, India, 500078, j.jaganmohan@hotmail.com

Juan E. N´apoles Vald´es, PhD (Math.), Prof., National University of the Northeast, Corrientes, 3400, Argentina; National Technological University, Resistencia, 3500, Argentina, jnapoles@exa.unne.edu.ar

For citation

Jonnalagadda J. M., Vald´es J. E. N. Positive Solutions of Nabla Fractional Sturm-Liouville Problems. The Bulletin of Irkutsk State University. Series Mathematics, 2025, vol. 51, pp. 50–65.

https://doi.org/10.26516/1997-7670.2025.51.50

Keywords
Riemann–Liouville fractional difference, Sturm–Liouville problem, cone, existence, positive solution
UDC
517.9
MSC
34A08, 39A12, 39A27
DOI
https://doi.org/10.26516/1997-7670.2025.51.50
References
  1. Ahrendt K., Castle L., Holm M., Yochman K. Laplace transforms for the nabladifference operator and a fractional variation of parameters formula. Commun. Appl. Anal., 2012, vol. 16, no. 3, pp. 317–347.
  2. Atici F.M., Atici M., Nguyen N., Zhoroev T., Koch G. A study on discrete and discrete fractional pharmacokinetics-pharmacodynamics models for tumor growth and anti-cancer effects. Comput. Math. Biophys., 2019, vol. 7, pp. 10–24.
  3. Bohner M., Jonnalagadda J.M. Discrete fractional cobweb models. Chaos Solitons Fractals, 2022, vol. 162, pp. 1–5.
  4. Eralp B., Topal F.S. Existence of positive solutions for discrete fractional boundary value problems. Adv. Dyn. Syst. Appl., 2020, vol. 15, no. 2, pp. 79–97.
  5. Ferreira R.A.C. Discrete fractional calculus and fractional difference equations. SpringerBriefs in Mathematics. Springer, Cham, 2022.
  6. Goodrich C., Peterson A.C. Discrete fractional calculus. Springer, Cham, 2015.
  7. Ikram A. Lyapunov inequalities for nabla Caputo boundary value problems. J. Difference Equ. Appl., 2019, vol. 25, no. 6, pp. 757–775.
  8. Jonnalagadda J.M. On two-point Riemann-Liouville type nabla fractional boundary value problems. Adv. Dyn. Syst. Appl., 2018, vol. 13, no. 2, pp. 141–166.
  9. Jonnalagadda J.M. A comparison result for the nabla fractional difference operator. Foundations, 2023, vol. 3, pp. 181–198.
  10. Ostalczyk P. Discrete fractional calculus. Applications in control and image processing. Series in Computer Vision, 4. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2016.
  11. St. Goar J. A Caputo boundary value problem in Nabla fractional calculus. Thesis (Ph.D.) The University of Nebraska-Lincoln, 2016.
  12. Guo D.J., Lakshmikantham V. Nonlinear problems in abstract cones. Notes and Reports in Mathematics in Science and Engineering, 5. Academic Press, Inc., Boston, MA, 1988.

Full text (english)