Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2025, Cilt: 8 Sayı: 1, 1 - 19, 31.01.2025
https://doi.org/10.33773/jum.1501013

Öz

Kaynakça

  • F. Jarad, E. Ugurlu, T. Abdeljawad, D. Baleanu, On a new class of fractional operators, Advance in Di_erence Equations, Vol.247, (2017).
  • K. Diethelm, The Analysis of Fractional Di_erential Equations, Lecture Notes in Mathematics, (2010).
  • R. Hilfer, Applications of Fractional Calculus in Physics, Word Scienti_c, Singapore, (2000).
  • A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Application of Fractional Differential Equations, North-Holland Matematics Studies, Vol. 204 (2006).
  • R.L. Magin, Fractional Calculus in Bioengineering, Begell House Publishers, Redding, (2006).
  • I. Podlubny, Fractional Di_erential Equations, Academic Press, San Diego, (1999).
  • S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon & Breach, Yverdon, (1993).
  • U.N. Katugampola, New approach to generalized fractional integral, Appl. Math. Comput., Vol.218, pp.860-865, (2011).
  • U.N Katugampola, A new approach to generalized fractional derivatives, Bull. Math. Anal. Appl., Vol.6, pp.1-15, (2014).
  • T. Abdeljawad, On conformable fractional calculus, J.Comput. Appl. Math., Vol.279, pp.57-66, (2015).
  • A.A Kilbas, Hadamard type fractional calculus, J. Korean Math. Soc., Vol.38, pp.1191-1204, (2001).
  • Y.Y. Gambo, F. Jarad, T. Abdeljawad, D. Baleanu, On Caputo modi_cation of the Hadamard fractional derivate. Adv. Di_er.Equ., Vol.2014, No.10 (2014).
  • F. Jarad, T. Abdeljawad, D. Baleanu, Caputo-type modi_cation of the Hadamard fractional derivative, Adv. Di_er. Equ., Vol.142 (2012).
  • Y. Adjabi, F. Jarad, D. Baleanu, T. Abdeljawad, On Cauchy problems with Caputo Hadamard fractional derivatives, J.Comput. Anal. Appl., Vol.21, No.1, pp.661-681 (2016).
  • F. Jarad, T. Abdeljawad, D. Baleanu, On the generalized fractional derivatives and their Caputo modi_cation. J., Nonlinear Sci. Appl., Vol.10, No.5, pp.2607-2619 (2017).
  • A. Akkurt, H. Yıldırım, On Hermite-Hadamard-Fej_er type inequalities for convex functions via fractional integrals, Mathematica Moravica, Vol.21, No.1, pp.105-123 (2017).
  • H. Yıldırım, Z. Kırtay, Ostrowski Inequality for Generalized Fractional Integral and Related Inequalities, Malaya Journal of Matematik, Vol.2, No.3, pp.322-329 (2014).
  • T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math., Vol.279, pp.57- 66 (2015).
  • L.G. Zivlaei, A.B. Mingarelli, On the Basic Theory of Some Generalized and Fractional Derivatives, Fractal and Fractional, Vol.6, No.672 (2022).
  • M. Tarıq, K.S. Ntouyas, A.A. Shaikh, New variant of Hermite-Hadamard, Fej_er and Pachpatte-Type Inequality and Its Re_nements Pertaining to Fractional Integral operator, Fractal and Fractional, Vol.7, No.405 (2023).
  • E. Kaçar, Z. Kaçar, H. Yıldırım, Integral inequalities for Riemann-Liouville Fractional Integral of a Function with Respeect to Another Function, Iran J. Matth Sci Inform. Vol.13, pp.1-13 (2018).

ON GENERALIZED CONFORMABLE FRACTIONAL OPERATORS

Yıl 2025, Cilt: 8 Sayı: 1, 1 - 19, 31.01.2025
https://doi.org/10.33773/jum.1501013

Öz

In this paper, we introduce the concepts of left and right generalized conformable fractional integrals, alongside the corresponding derivatives.
Additionally, we extend our investigation to derive the generalized conformable derivatives for functions within specific spaces, elucidating their inherent properties.

Kaynakça

  • F. Jarad, E. Ugurlu, T. Abdeljawad, D. Baleanu, On a new class of fractional operators, Advance in Di_erence Equations, Vol.247, (2017).
  • K. Diethelm, The Analysis of Fractional Di_erential Equations, Lecture Notes in Mathematics, (2010).
  • R. Hilfer, Applications of Fractional Calculus in Physics, Word Scienti_c, Singapore, (2000).
  • A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Application of Fractional Differential Equations, North-Holland Matematics Studies, Vol. 204 (2006).
  • R.L. Magin, Fractional Calculus in Bioengineering, Begell House Publishers, Redding, (2006).
  • I. Podlubny, Fractional Di_erential Equations, Academic Press, San Diego, (1999).
  • S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon & Breach, Yverdon, (1993).
  • U.N. Katugampola, New approach to generalized fractional integral, Appl. Math. Comput., Vol.218, pp.860-865, (2011).
  • U.N Katugampola, A new approach to generalized fractional derivatives, Bull. Math. Anal. Appl., Vol.6, pp.1-15, (2014).
  • T. Abdeljawad, On conformable fractional calculus, J.Comput. Appl. Math., Vol.279, pp.57-66, (2015).
  • A.A Kilbas, Hadamard type fractional calculus, J. Korean Math. Soc., Vol.38, pp.1191-1204, (2001).
  • Y.Y. Gambo, F. Jarad, T. Abdeljawad, D. Baleanu, On Caputo modi_cation of the Hadamard fractional derivate. Adv. Di_er.Equ., Vol.2014, No.10 (2014).
  • F. Jarad, T. Abdeljawad, D. Baleanu, Caputo-type modi_cation of the Hadamard fractional derivative, Adv. Di_er. Equ., Vol.142 (2012).
  • Y. Adjabi, F. Jarad, D. Baleanu, T. Abdeljawad, On Cauchy problems with Caputo Hadamard fractional derivatives, J.Comput. Anal. Appl., Vol.21, No.1, pp.661-681 (2016).
  • F. Jarad, T. Abdeljawad, D. Baleanu, On the generalized fractional derivatives and their Caputo modi_cation. J., Nonlinear Sci. Appl., Vol.10, No.5, pp.2607-2619 (2017).
  • A. Akkurt, H. Yıldırım, On Hermite-Hadamard-Fej_er type inequalities for convex functions via fractional integrals, Mathematica Moravica, Vol.21, No.1, pp.105-123 (2017).
  • H. Yıldırım, Z. Kırtay, Ostrowski Inequality for Generalized Fractional Integral and Related Inequalities, Malaya Journal of Matematik, Vol.2, No.3, pp.322-329 (2014).
  • T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math., Vol.279, pp.57- 66 (2015).
  • L.G. Zivlaei, A.B. Mingarelli, On the Basic Theory of Some Generalized and Fractional Derivatives, Fractal and Fractional, Vol.6, No.672 (2022).
  • M. Tarıq, K.S. Ntouyas, A.A. Shaikh, New variant of Hermite-Hadamard, Fej_er and Pachpatte-Type Inequality and Its Re_nements Pertaining to Fractional Integral operator, Fractal and Fractional, Vol.7, No.405 (2023).
  • E. Kaçar, Z. Kaçar, H. Yıldırım, Integral inequalities for Riemann-Liouville Fractional Integral of a Function with Respeect to Another Function, Iran J. Matth Sci Inform. Vol.13, pp.1-13 (2018).
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Operatör Cebirleri ve Fonksiyonel Analiz
Bölüm Araştırma Makalesi
Yazarlar

Sümeyye Ermeydan Çiriş 0009-0000-2472-5311

Huseyin Yıldırım 0000-0001-8855-9260

Yayımlanma Tarihi 31 Ocak 2025
Gönderilme Tarihi 24 Haziran 2024
Kabul Tarihi 28 Ocak 2025
Yayımlandığı Sayı Yıl 2025 Cilt: 8 Sayı: 1

Kaynak Göster

APA Ermeydan Çiriş, S., & Yıldırım, H. (2025). ON GENERALIZED CONFORMABLE FRACTIONAL OPERATORS. Journal of Universal Mathematics, 8(1), 1-19. https://doi.org/10.33773/jum.1501013
AMA Ermeydan Çiriş S, Yıldırım H. ON GENERALIZED CONFORMABLE FRACTIONAL OPERATORS. JUM. Ocak 2025;8(1):1-19. doi:10.33773/jum.1501013
Chicago Ermeydan Çiriş, Sümeyye, ve Huseyin Yıldırım. “ON GENERALIZED CONFORMABLE FRACTIONAL OPERATORS”. Journal of Universal Mathematics 8, sy. 1 (Ocak 2025): 1-19. https://doi.org/10.33773/jum.1501013.
EndNote Ermeydan Çiriş S, Yıldırım H (01 Ocak 2025) ON GENERALIZED CONFORMABLE FRACTIONAL OPERATORS. Journal of Universal Mathematics 8 1 1–19.
IEEE S. Ermeydan Çiriş ve H. Yıldırım, “ON GENERALIZED CONFORMABLE FRACTIONAL OPERATORS”, JUM, c. 8, sy. 1, ss. 1–19, 2025, doi: 10.33773/jum.1501013.
ISNAD Ermeydan Çiriş, Sümeyye - Yıldırım, Huseyin. “ON GENERALIZED CONFORMABLE FRACTIONAL OPERATORS”. Journal of Universal Mathematics 8/1 (Ocak 2025), 1-19. https://doi.org/10.33773/jum.1501013.
JAMA Ermeydan Çiriş S, Yıldırım H. ON GENERALIZED CONFORMABLE FRACTIONAL OPERATORS. JUM. 2025;8:1–19.
MLA Ermeydan Çiriş, Sümeyye ve Huseyin Yıldırım. “ON GENERALIZED CONFORMABLE FRACTIONAL OPERATORS”. Journal of Universal Mathematics, c. 8, sy. 1, 2025, ss. 1-19, doi:10.33773/jum.1501013.
Vancouver Ermeydan Çiriş S, Yıldırım H. ON GENERALIZED CONFORMABLE FRACTIONAL OPERATORS. JUM. 2025;8(1):1-19.