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Year 2019, Volume 9, Issue 4, 792 - 799, 01.12.2019

Abstract

References

  • Abdeljawad, T (2015), On conformable fractional calculus, Journal of Computational and Applied Mathematics 279, pp. 57–66.
  • Anderson, D. R. (2016), Taylor’s formula and integral inequalities for conformable fractional deriva- tives, Contributions in Mathematics and Engineering, in Honor of Constantin Caratheodory, Springer, New York.
  • Hammad M. A. and Khalil R. (2014), Conformable fractional heat differential equations, International Journal of Differential Equations and Applications 13( 3), pp. 177-183.
  • Hammad M. A. and Khalil R. (2014), Abel’s formula and wronskian for conformable fractional differ- ential equations, International Journal of Differential Equations and Applications 13(3), pp. 177-183.
  • Iyiola O.S.and Nwaeze E.R.(2016), Some new results on the new conformable fractional calculus with application using D’Alambert approach, Progr. Fract. Differ. Appl., 2(2), pp.115-122.
  • Khalil R., Al horani M., Yousef A. and Sababheh M.(2014), A new definition of fractional derivative, Journal of Computational Apllied Mathematics, 264, pp. 65-70.
  • Katugampola U.N. (2011), New approach to a generalized fractional integral, Appl. Math. Comput., 218(3), pp. 860–865.
  • Katugampola U.N. (2014), New approach to generalized fractional derivatives, B. Math. Anal. App., 6(4), pp. 1–15.
  • Kilbas A. A., Srivastava H.M. and Trujillo J.J. (2016), Theory and Applications of Fractional Differ- ential Equations, Elsevier B.V., Amsterdam, Netherlands.
  • Samko, S.G., Kilbas, A.A. and Marichev, O.I. (1993), Fractional Integrals and Derivatives: Theory and Applications, Yverdon: Gordon and Breach.

ON GENERALIZED THE CONFORMABLE FRACTIONAL CALCULUS

Year 2019, Volume 9, Issue 4, 792 - 799, 01.12.2019

Abstract

In this paper, we generalize the conformable fractional derivative and integral and obtain several results such as the product rule, quotient rule, chain rule.

References

  • Abdeljawad, T (2015), On conformable fractional calculus, Journal of Computational and Applied Mathematics 279, pp. 57–66.
  • Anderson, D. R. (2016), Taylor’s formula and integral inequalities for conformable fractional deriva- tives, Contributions in Mathematics and Engineering, in Honor of Constantin Caratheodory, Springer, New York.
  • Hammad M. A. and Khalil R. (2014), Conformable fractional heat differential equations, International Journal of Differential Equations and Applications 13( 3), pp. 177-183.
  • Hammad M. A. and Khalil R. (2014), Abel’s formula and wronskian for conformable fractional differ- ential equations, International Journal of Differential Equations and Applications 13(3), pp. 177-183.
  • Iyiola O.S.and Nwaeze E.R.(2016), Some new results on the new conformable fractional calculus with application using D’Alambert approach, Progr. Fract. Differ. Appl., 2(2), pp.115-122.
  • Khalil R., Al horani M., Yousef A. and Sababheh M.(2014), A new definition of fractional derivative, Journal of Computational Apllied Mathematics, 264, pp. 65-70.
  • Katugampola U.N. (2011), New approach to a generalized fractional integral, Appl. Math. Comput., 218(3), pp. 860–865.
  • Katugampola U.N. (2014), New approach to generalized fractional derivatives, B. Math. Anal. App., 6(4), pp. 1–15.
  • Kilbas A. A., Srivastava H.M. and Trujillo J.J. (2016), Theory and Applications of Fractional Differ- ential Equations, Elsevier B.V., Amsterdam, Netherlands.
  • Samko, S.G., Kilbas, A.A. and Marichev, O.I. (1993), Fractional Integrals and Derivatives: Theory and Applications, Yverdon: Gordon and Breach.

Details

Primary Language English
Journal Section Research Article
Authors

M. Z. SARIKAYA This is me
Department of Mathematics, Faculty of Science and Arts, D¨uzce University, D¨uzce-TURKEY.


H. BUDAK This is me
Department of Mathematics, Faculty of Science and Arts, D¨uzce University, D¨uzce-TURKEY.


H. USTA This is me
Department of Mathematics, Faculty of Science and Arts, D¨uzce University, D¨uzce-TURKEY.

Publication Date December 1, 2019
Published in Issue Year 2019, Volume 9, Issue 4

Cite

Bibtex @ { twmsjaem760951, journal = {TWMS Journal of Applied and Engineering Mathematics}, issn = {2146-1147}, eissn = {2587-1013}, address = {Işık University ŞİLE KAMPÜSÜ Meşrutiyet Mahallesi, Üniversite Sokak No:2 Şile / İstanbul}, publisher = {Turkic World Mathematical Society}, year = {2019}, volume = {9}, number = {4}, pages = {792 - 799}, title = {ON GENERALIZED THE CONFORMABLE FRACTIONAL CALCULUS}, key = {cite}, author = {Sarıkaya, M. Z. and Budak, H. and Usta, H.} }