Year 2021, Volume 4 , Issue 1, Pages 73 - 80 2021-01-31

SPECTRAL PROPERTIES OF A CONFORMABLE BOUNDARY VALUE PROBLEM ON TIME SCALES

Zeki CEYLAN [1]


We study a self-adjoint conformable dynamic equation of second order on an arbitrary time scale $\mathbb{T}$. We state an existence and uniqueness theorem for the solutions of this equation. We prove the conformable Lagrange identity on time scales. Then, we consider a conformable eigenvalue problem generated by the above-mentioned dynamic equation of second order and we examine some of the spectral properties of this boundary value problem.
Time scales, Conformable derivative
  • Referans1 T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics, 279(2015), 57-66.
  • Referans2 M. Abu Hammad, R. Khalil, Abel's formula and Wronskian for conformable fractional differential equations, Internat. J. Diff. Equ. Appl., 13(2014), No. 3, 177-183.
  • Referans3 M. Abu Hammad, R. Khalil, Conformable fractional heat differential equations, Internat. J. Pure Appl. Math., 94(2014), No. 2, 215-221.
  • Referans4 H. Abu-Shaab, R. Khalil, Solution of some conformable fractional differential equations, Int. J. Pure Appl. Math., 103(2015), No. 4, 667-673.
  • Referans5 M. J. Lazo, D. F. M. Torres, Variational calculus with conformable fractional derivatives, IEEE/CAA Journal of Automatica Sinica, 4(April 2017), No. 2.
  • Referans6 W. Rosa, J. Weberspil, Dual conformable derivative:Definition, simple properties and perspectives for applications, Chaos, Solitons and Fractals, 117(2018), 137-141.
  • Referans7 D. Anderson, R. I. Avery, Fractional-order boundary value problem with Sturm-Liouville boundary conditions, Electronic Journal of Differential Equations, 29(2015), 1-10.
  • Referans8 H. Batarfi, J. Losada, J. J. Nieto, W. Shammakh, Three-point boundary value problems for conformable fractional differential equations, Journal of Function Spaces, Volume 2015, Article ID 706383, 6 pages, doi:10.1155/2015/706383.
  • Referans9 B. P. Allahverdiev, H. Tuna, Y. Yalcinkaya, Conformable fractional Sturm-Liouville equation, Math. Meth. Appl. Sci., 42(2019), 3508-3526.
  • Referans10 N. Benkhettou, S. Hassani, D. F. M. Torres, A conformable fractional calculus on arbitrary time scales, Journal of King Saud University-Science, 28(2016), 93-98.
  • Referans11 M. Bohner, V. F. Hatipoğlu, Dynamic Cobweb models with conformable fractional derivatives, Nonlinear Anal., Hybrid Syst. 32(2019), 157-167.
  • Referans12 T. Gulsen, E. Yilmaz, S. Goktas, Conformable fractional Dirac system on time scales, J. Inequal. Appl., 2017:10, 2017.
  • Referans13 T. Gulsen, E. Yilmaz, H. Kemaloglu, Conformable fractional Sturm-Liouville equation and some existence results on time scales, Turk. J. Math. 42(2018), No. 3, 1348-1360.
  • Referans14 S. Rahmat, M. Rafi, A new definition of conformable fractional derivative on arbitrary time scales, Adv. Difference Equ., 2019:354, 2019.
  • Referans15 D. F. Zhou, X. X. You, A new fractional derivative on time scales, Adv. Appl. Math. Anal., 11(2016), No. 1, 1-9.
  • Referans16 C. Zhang, S. Sun, Sturm-Picone comparison theorem of a kind of conformable fractional differential equations on time scales, J. Appl. math. Comput., 55(2017), 191-203, doi:10.1007/s12190-016-1032-9.
  • Referans17 M. Bohner, A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Birkhauser, Boston Inc. Boston, MA, 2001.
Primary Language en
Subjects Mathematics
Journal Section Research Article
Authors

Author: Zeki CEYLAN (Primary Author)
Institution: MERSİN ÜNİVERSİTESİ
Country: Turkey


Dates

Application Date : February 28, 2020
Acceptance Date : February 20, 2021
Publication Date : January 31, 2021

Bibtex @research article { jum695777, journal = {Journal of Universal Mathematics}, issn = {2618-5660}, eissn = {2618-5660}, address = {editorinchief@junimath.com}, publisher = {Gökhan ÇUVALCIOĞLU}, year = {2021}, volume = {4}, pages = {73 - 80}, doi = {10.33773/jum.695777}, title = {SPECTRAL PROPERTIES OF A CONFORMABLE BOUNDARY VALUE PROBLEM ON TIME SCALES}, key = {cite}, author = {Ceylan, Zeki} }
APA Ceylan, Z . (2021). SPECTRAL PROPERTIES OF A CONFORMABLE BOUNDARY VALUE PROBLEM ON TIME SCALES . Journal of Universal Mathematics , 4 (1) , 73-80 . DOI: 10.33773/jum.695777
MLA Ceylan, Z . "SPECTRAL PROPERTIES OF A CONFORMABLE BOUNDARY VALUE PROBLEM ON TIME SCALES" . Journal of Universal Mathematics 4 (2021 ): 73-80 <https://dergipark.org.tr/en/pub/jum/issue/60411/695777>
Chicago Ceylan, Z . "SPECTRAL PROPERTIES OF A CONFORMABLE BOUNDARY VALUE PROBLEM ON TIME SCALES". Journal of Universal Mathematics 4 (2021 ): 73-80
RIS TY - JOUR T1 - SPECTRAL PROPERTIES OF A CONFORMABLE BOUNDARY VALUE PROBLEM ON TIME SCALES AU - Zeki Ceylan Y1 - 2021 PY - 2021 N1 - doi: 10.33773/jum.695777 DO - 10.33773/jum.695777 T2 - Journal of Universal Mathematics JF - Journal JO - JOR SP - 73 EP - 80 VL - 4 IS - 1 SN - 2618-5660-2618-5660 M3 - doi: 10.33773/jum.695777 UR - https://doi.org/10.33773/jum.695777 Y2 - 2021 ER -
EndNote %0 Journal of Universal Mathematics SPECTRAL PROPERTIES OF A CONFORMABLE BOUNDARY VALUE PROBLEM ON TIME SCALES %A Zeki Ceylan %T SPECTRAL PROPERTIES OF A CONFORMABLE BOUNDARY VALUE PROBLEM ON TIME SCALES %D 2021 %J Journal of Universal Mathematics %P 2618-5660-2618-5660 %V 4 %N 1 %R doi: 10.33773/jum.695777 %U 10.33773/jum.695777
ISNAD Ceylan, Zeki . "SPECTRAL PROPERTIES OF A CONFORMABLE BOUNDARY VALUE PROBLEM ON TIME SCALES". Journal of Universal Mathematics 4 / 1 (January 2021): 73-80 . https://doi.org/10.33773/jum.695777
AMA Ceylan Z . SPECTRAL PROPERTIES OF A CONFORMABLE BOUNDARY VALUE PROBLEM ON TIME SCALES. JUM. 2021; 4(1): 73-80.
Vancouver Ceylan Z . SPECTRAL PROPERTIES OF A CONFORMABLE BOUNDARY VALUE PROBLEM ON TIME SCALES. Journal of Universal Mathematics. 2021; 4(1): 73-80.
IEEE Z. Ceylan , "SPECTRAL PROPERTIES OF A CONFORMABLE BOUNDARY VALUE PROBLEM ON TIME SCALES", Journal of Universal Mathematics, vol. 4, no. 1, pp. 73-80, Jan. 2021, doi:10.33773/jum.695777