Araştırma Makalesi
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SPECTRAL PROPERTIES OF A CONFORMABLE BOUNDARY VALUE PROBLEM ON TIME SCALES

Yıl 2021, Cilt: 4 Sayı: 1, 73 - 80, 31.01.2021

Zeki Ceylan

https://doi.org/10.33773/jum.695777
Cited By: 1

Öz

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.

Anahtar Kelimeler

Time scales Conformable derivative

Kaynakça

  • 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.

Yıl 2021, Cilt: 4 Sayı: 1, 73 - 80, 31.01.2021

Zeki Ceylan

https://doi.org/10.33773/jum.695777
Cited By: 1

Öz

Kaynakça

  • 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.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Zeki Ceylan

Yayımlanma Tarihi 31 Ocak 2021
Gönderilme Tarihi 28 Şubat 2020
Kabul Tarihi 20 Şubat 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 4 Sayı: 1

Kaynak Göster

APA Ceylan, Z. (2021). SPECTRAL PROPERTIES OF A CONFORMABLE BOUNDARY VALUE PROBLEM ON TIME SCALES. Journal of Universal Mathematics, 4(1), 73-80. https://doi.org/10.33773/jum.695777
AMA Ceylan Z. SPECTRAL PROPERTIES OF A CONFORMABLE BOUNDARY VALUE PROBLEM ON TIME SCALES. JUM. Ocak 2021;4(1):73-80. doi:10.33773/jum.695777
Chicago Ceylan, Zeki. “SPECTRAL PROPERTIES OF A CONFORMABLE BOUNDARY VALUE PROBLEM ON TIME SCALES”. Journal of Universal Mathematics 4, sy. 1 (Ocak 2021): 73-80. https://doi.org/10.33773/jum.695777.
EndNote Ceylan Z (01 Ocak 2021) SPECTRAL PROPERTIES OF A CONFORMABLE BOUNDARY VALUE PROBLEM ON TIME SCALES. Journal of Universal Mathematics 4 1 73–80.
IEEE Z. Ceylan, “SPECTRAL PROPERTIES OF A CONFORMABLE BOUNDARY VALUE PROBLEM ON TIME SCALES”, JUM, c. 4, sy. 1, ss. 73–80, 2021, doi: 10.33773/jum.695777.
ISNAD Ceylan, Zeki. “SPECTRAL PROPERTIES OF A CONFORMABLE BOUNDARY VALUE PROBLEM ON TIME SCALES”. Journal of Universal Mathematics 4/1 (Ocak2021), 73-80. https://doi.org/10.33773/jum.695777.
JAMA Ceylan Z. SPECTRAL PROPERTIES OF A CONFORMABLE BOUNDARY VALUE PROBLEM ON TIME SCALES. JUM. 2021;4:73–80.
MLA Ceylan, Zeki. “SPECTRAL PROPERTIES OF A CONFORMABLE BOUNDARY VALUE PROBLEM ON TIME SCALES”. Journal of Universal Mathematics, c. 4, sy. 1, 2021, ss. 73-80, doi:10.33773/jum.695777.
Vancouver Ceylan Z. SPECTRAL PROPERTIES OF A CONFORMABLE BOUNDARY VALUE PROBLEM ON TIME SCALES. JUM. 2021;4(1):73-80.

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