Research Article
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Year 2025, , 1 - 19, 31.01.2025
https://doi.org/10.33773/jum.1501013

Abstract

References

  • 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

Year 2025, , 1 - 19, 31.01.2025
https://doi.org/10.33773/jum.1501013

Abstract

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.

References

  • 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).
There are 21 citations in total.

Details

Primary Language English
Subjects Operator Algebras and Functional Analysis
Journal Section Research Article
Authors

Sümeyye Ermeydan Çiriş 0009-0000-2472-5311

Huseyin Yıldırım 0000-0001-8855-9260

Publication Date January 31, 2025
Submission Date June 24, 2024
Acceptance Date January 28, 2025
Published in Issue Year 2025

Cite

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. January 2025;8(1):1-19. doi:10.33773/jum.1501013
Chicago Ermeydan Çiriş, Sümeyye, and Huseyin Yıldırım. “ON GENERALIZED CONFORMABLE FRACTIONAL OPERATORS”. Journal of Universal Mathematics 8, no. 1 (January 2025): 1-19. https://doi.org/10.33773/jum.1501013.
EndNote Ermeydan Çiriş S, Yıldırım H (January 1, 2025) ON GENERALIZED CONFORMABLE FRACTIONAL OPERATORS. Journal of Universal Mathematics 8 1 1–19.
IEEE S. Ermeydan Çiriş and H. Yıldırım, “ON GENERALIZED CONFORMABLE FRACTIONAL OPERATORS”, JUM, vol. 8, no. 1, pp. 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 (January 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 and Huseyin Yıldırım. “ON GENERALIZED CONFORMABLE FRACTIONAL OPERATORS”. Journal of Universal Mathematics, vol. 8, no. 1, 2025, pp. 1-19, doi:10.33773/jum.1501013.
Vancouver Ermeydan Çiriş S, Yıldırım H. ON GENERALIZED CONFORMABLE FRACTIONAL OPERATORS. JUM. 2025;8(1):1-19.