International Scientific Journal

Authors of this Paper

External Links


In study, we show the existence and integral representation of solution for energy-dependent fractional Sturm-Liouville impulsive problem of order with α(1,2] impulsive and boundary conditions. An existence theorem is proved for energy-dependent fractional Sturm-Liouville impulsive problem by using Schaefer fixed point theorem. Furthermore, in the last part of the article, an application is given for the problem and visual results are shown by figures.
PAPER REVISED: 2018-11-01
PAPER ACCEPTED: 2018-11-07
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Supplement 1, PAGES [S139 - S152]
  1. Levitan, B. M. Sargsjan, I. S., Introduction to Spektral Theory: Selfadjoint Ordinary Differential Opera-tors, American Math. Soc., Providence, R.I., USA, 1975
  2. Zettl, A., Sturm-Liouville Theory, Mathematical Surveys and Monographs, American Mathematical Soci-ety, Providence, R.I., USA, 2005
  3. Yilmaz, E., Lipschitz Stability of Inverse Nodal Problem for Energy-Dependent Sturm-Liouville Equa-tion, New Trends in Mathematical Sciences, 1 (2015), 1, pp. 46-61
  4. Panakhov, E., Yılmazer, R., A Hochstadt-Lieberman Theorem for the Hydrogen Atom Equation, Applied and Computational Mathematics, 11 (2012), 1, pp. 74-80
  5. Klimek, M., Argawal, O. P., On a Regular Fractional Sturm-Liouville Problem with Derivatives of Order in (0,1), Proceedings, 13th International Carpathian Control Conference, Vysoke Tatry (Podbanske), Slo-vakia, 2012
  6. Klimek, M., Argawal, O. P., Fractional Sturm-Liouville Problem, Computers and Mathematics with Ap-plications, 66 (2013), 5, pp. 795-812
  7. Zayernouri, M., Karniadakis, G. E., Fractional Sturm-Liouville Eigen-Problems: Theory and Numerical Approximation, Journal of Computational Physics, 252 (2013), 1, pp. 495-517
  8. Bas, E., Fundamental Spectral Theory of Fractional Singular Sturm-Liouville Operator, Journal of Func. Spaces and Appl., 2013 (2013), ID 915830
  9. Bas, E., Metin, F., Fractional Singular Sturm-Liouville Operator for Coulomb Potential, Advances in Differences Equations, 2013 (2013), 1, 300
  10. Bas, E., Metin, F., An Application of Comparison Criteria to Fractional Spectral Problem Having Cou-lomb Potential, Thermal Science, 22 (2018), Suppl. 1, pp. S79-S85
  11. Dehghan, M., Mingarelli, A. B., Fractional Sturm-Liouville Eigenvalue Problems I, On-line first, arX-iv:1712.09891v1, 2017
  12. Ciesielski, M., et al., The Fractional Sturm Liouville Problem Numerical Approximation and Applica-tion in Fractional Diffusion, Journal of Computational and Applied Mathematics, 317 (2017), June, pp. 573-588
  13. Milman, V. D., Myshkis, A. D., On The Stability of Motion in the Presence of Impulses (in Russian), Siberian Mathematical Journal, 1 (1960), 2, pp. 233-237
  14. Lakshmikantham, V., et al., Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989
  15. Dishlieva, K., Impulsive Differential Equations and Applications, Applied & Computational Mathemat-ics, 1 (2012), 6, pp. 1-3
  16. Baleanu, D., et al., Fractional Dynamics and Control, Springer-Verlag, Berlin, 2012
  17. Kilbas, A. A., et al., Theory and Applications of Fractional Differential Equations, North-Holland Math-ematics Studies, Elsevier, Amsterdam, The Netherlands, 2006
  18. Bayram, M, et al., A Solution Method for Integro- Differential Equations of Comformable Fractional, Thermal Science, 22 (2018), Suppl. 1, pp. S7-S14
  19. Inc, M., et al., New Trends in Fractional Modelling of Transport Problems in Fluid Mechanics and Heat Mass Transfer, Thermal Science, 22 (2018), Suppl. 1, pp. SIX-SX
  20. Srivastava, H. M., et al., Some Remarks on the Paper, Entitled “Fractional and Operational Calculus with Generalized Fractional Derivative Operators and Mittag-Leffler Type Functions”, TWMS Journal of Pure and Applied Mathematics, 8 (2017), 1, pp. 112-114
  21. Samoilenko, A. M., Perestyuk, N. A., Impulsive Differential Equations, World Scientific, Singapore, 1995
  22. Zavalishchin, S. T., Sesekin, A. N., Dynamic Impulse Systems: Theory and Applications, Kluwer Academ-ic Publishers Group, Dordrecht, Germany, 1997
  23. Zhang, S., Positive Solutions for Baundary-Value Problems of Nonlinear Fractional Differential Equa-tions, Electronic Journal of Differential Equations, 36 (2006), 2, pp. 1-12
  24. Tian, Y., Bai, Z., Existence Results for the Three-Point Impulsive Boundary Value Problem Involving Fractional Differential Equations, Computers and Mathematics with Applications, 59 (2010), 8, pp. 2601-2609
  25. Ahmad, B., Nieto, J. J., Existence of Solutions for Impulsive Anti-Periodic Boundary Value Problems of Fractional Order, Taiwanese Journal of Mathematics, 15 (2011), 3, pp. 981-993
  26. Agarwal, R. P., et al., Existence Results for Differential Equations with Fractional Order and Impulses, Memoirs on Differential Equations and Mathematical Physics, 44 (2008), Jan., pp. 1-21
  27. Zhou, J., Feng, M., Green’s Function for Sturm-Liouville-Type Boundary Value Problems of Fractional Order Impulsive Differential Equations and its Applications, Boundary Value Problems, 2014 (2014), 1, 69
  28. Zeidler, E., Nonlinear Functional Analysis and Its Applications-I: Fixed-Point Theorems, Springer, New York, USA, 1986

© 2020 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence