ON k-CONFORMABLE FRACTIONAL OPERATORS

Year 2024, Volume: 7 Issue: 1, 12 - 28, 31.01.2024

Sümeyye Ermeydan Çiriş Huseyin Yıldırım

https://doi.org/10.33773/jum.1335668

Cited By: 1

Abstract

In this study, we define the left and right fractional kconformable
integrals and derivatives. Furthermore, we obtained the fractional kconformable
derivatives of functions associated with some spaces and express their properties.

Keywords

conformable derivatives, fractional conformable integrals, fractional conformable derivatives .

References

• F. Jarad, E. Ugurlu, T. Abdeljawad, D. Baleanu, On A New Class Of Fractional Operators, Advance in Difference Equations, Vol.247 (2017).
• K. Diethelm, The Analysis of Fractional Differential Equations, Lecture Notes in Mathematics, (2010).
• R. Hilfer, Applications of Fractional Calculus in Physics, Word Scientific, 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 Differential Equations, Academic Press, San Diego, (1999).
• S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and 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 Modification Of The Hadamard Fractional Derivate, Adv. Differ.Equ., Vol.10, (2014).
• F. Jarad, T. Abdeljawad, D. Baleanu, Caputo-Type Modification Of The Hadamard Fractional Derivative, Adv. Differ. 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 Modification, J., Nonlinear Sci. Appl., Vol.10, No.5, pp.2607-2619 (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).