(k, s)-Riemann-Liouville fractional integral and applications

KIRIS, Mehmet Eyüp; Sarikaya, Mehmet; AHMAD, FAROOQ; DAHMANI, Zoubir

(k, s)-Riemann-Liouville fractional integral and applications

Mehmet Zeki SARIKAYA, (Düzce Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Düzce, Türkiye)

Zoubir DAHMANI, (Laboratory of Pure and Applied Mathematics, UMAB, University of Mostaganem, Algeria,)

Mehmet Eyüp KIRIS, (Afyon Kocatepe Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Afyon, Türkiye)

Farooq AHMAD (Mathematics Department, Colleege of Science, Majmaah University, Al-Zulfi, Kingdom of Saudi Arabia,)

Hacettepe Journal of Mathematics and Statistics

3 1

Yıl: 2016 Cilt: 45 Sayı: 1 Sayfa Aralığı: 77 - 89 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

(k, s)-Riemann-Liouville fractional integral and applications

Öz:

In this paper, we introduce a new approach on fractional integration,which generalizes the Riemann-Liouville fractional integral. We provesome properties for this new approach. We also establish some newintegral inequalities using this new fractional integration.

Anahtar Kelime:

Konular: Matematik İstatistik ve Olasılık

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

Belarbi, S. and Dahmani, Z., On some new fractional integral inequalities, J. Ineq. Pure and Appl. Math., 10(3) (2009), Art. 86.
Dahmani, Z., New inequalities in fractional integrals, International Journal of Nonlinear Scinece, 9(4) (2010), 493-497.
Dahmani, Z., On Minkowski and Hermite-Hadamard integral inequalities via fractional in- tegration, Ann. Funct. Anal. 1(1) (2010), 51-58.
Dahmani, Z., Tabharit, L. and Taf, S., Some fractional integral inequalities, Nonl. Sci. Lett. A, 1(2) (2010), 155-160.
Dahmani, Z., Tabharit, L. and Taf, S., New generalizations of Gruss inequality usin Riemann-Liouville fractional integrals, Bull. Math. Anal. Appl., 2(3) (2010), 93-99.
Diaz, R. and Pariguan, E., On hypergeometric functions and Pochhammer k-symbol, Di- vulg.Math, 15.(2007),179-192.
Gorenflo, R. and Mainardi, F., Fractional calculus: integral and differential equations of fractional order, Springer Verlag, Wien (1997), 223-276.
Kilbas, A. A.,Srivastava, H. M. and Trujillo, J. J., Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204, Elsevier Sci. B.V., Ams- terdam, 2006.
Hadamard, J., Essai sur l'étude des fonctions données par leur développement de Taylor,Jour.PureandAppl.Math4(8),1892,101-186.
Katugompola, U.N., New Approach Generalized Fractional Integral, Applied Math and Comp. 218(2011),860-865.
Latif, M. A. and Hussain, S., New inequalities of Ostrowski type for co-ordineted convex functions via fractional integrals, Journal of Fractional Calculus and Applications,Vol. 2., 2012, No. 9, pp. 1-15.
Miller, S. and Ross, B., An introduction to the Fractional Calculus and Fractional Differ- ential Equations, John Wiley & Sons, USA, 1993, p.2.
Mubeen, S. and Habibullah, G.M., k-fractional integrals and application, Int. J. Contemp. Math. Sciences, 7(2), 2012, 89-94.
Romero, L. G., Luque, L. L., Dorrego, G. A. and Cerutti, R. A., On the k-Riemann- Liouville Fractional Derivative, Int. J. Contemp. Math. Sciences, 8(1), 2013, 41-51.
Sarikaya, M.Z. and Ogunmez, H., On new inequalities via Riemann-Liouville fractional integration, Abstract and Applied Analysis, Volume 2012, Article ID 428983, 10 pages, doi:10.1155/2012/428983.
Sarikaya, M. Z., Set, E., Yaldiz, H. and Basak, N., Hermite -Hadamard's inequalities for fractional integrals and related fractional inequalities, Mathematical and Computer Mod- elling, 57 (2013) 2403-2407.
Sarikaya, M. Z., On the Hermite-Hadamard-type inequalities for co-ordinated convex func- tion via fractional integrals, Integral Transforms and Special Functions, Volume 25, Issue 2, pp:134-147, 2014.
Sarikaya, M. Z., Ostrowski type inequalities involving the right Caputo fractional derivatives belong to Lp, Facta Universitatis, Series Mathematics and Informatics , Vol. 27 No 2 (2012), 191-197.
Sarikaya, M. Z. and Yaldiz, H., On weighted Montogomery identities for Riemann-Liouville fractional integrals, Konuralp Journal of Mathematics, Volume 1 No. 1 pp. 48-53, 2013.
Sarikaya, M. Z., and Karaca, A., On the k-Riemann-Liouville fractional integral and appli- cations, International Journal of Statistics and Mathematics, Vol. 1(1), pp. 022-032, August, 2014.
Tunc, M., On new inequalities for h-convex functions via Riemann-Liouville fractional integration, Filomat 27:4 (2013), 559-565
Samko, S. G., Kilbas, A. A and Marichev, O. I., Fractional Integrals and Derivatives Theory and Application, Gordan and Breach Science, New York, 1993.

APA	Sarikaya M, DAHMANI Z, KIRIS M, AHMAD F (2016). (k, s)-Riemann-Liouville fractional integral and applications. , 77 - 89.
Chicago	Sarikaya Mehmet,DAHMANI Zoubir,KIRIS Mehmet Eyüp,AHMAD FAROOQ (k, s)-Riemann-Liouville fractional integral and applications. (2016): 77 - 89.
MLA	Sarikaya Mehmet,DAHMANI Zoubir,KIRIS Mehmet Eyüp,AHMAD FAROOQ (k, s)-Riemann-Liouville fractional integral and applications. , 2016, ss.77 - 89.
AMA	Sarikaya M,DAHMANI Z,KIRIS M,AHMAD F (k, s)-Riemann-Liouville fractional integral and applications. . 2016; 77 - 89.
Vancouver	Sarikaya M,DAHMANI Z,KIRIS M,AHMAD F (k, s)-Riemann-Liouville fractional integral and applications. . 2016; 77 - 89.
IEEE	Sarikaya M,DAHMANI Z,KIRIS M,AHMAD F "(k, s)-Riemann-Liouville fractional integral and applications." , ss.77 - 89, 2016.
ISNAD	Sarikaya, Mehmet vd. "(k, s)-Riemann-Liouville fractional integral and applications". (2016), 77-89.

APA	Sarikaya M, DAHMANI Z, KIRIS M, AHMAD F (2016). (k, s)-Riemann-Liouville fractional integral and applications. Hacettepe Journal of Mathematics and Statistics, 45(1), 77 - 89.
Chicago	Sarikaya Mehmet,DAHMANI Zoubir,KIRIS Mehmet Eyüp,AHMAD FAROOQ (k, s)-Riemann-Liouville fractional integral and applications. Hacettepe Journal of Mathematics and Statistics 45, no.1 (2016): 77 - 89.
MLA	Sarikaya Mehmet,DAHMANI Zoubir,KIRIS Mehmet Eyüp,AHMAD FAROOQ (k, s)-Riemann-Liouville fractional integral and applications. Hacettepe Journal of Mathematics and Statistics, vol.45, no.1, 2016, ss.77 - 89.
AMA	Sarikaya M,DAHMANI Z,KIRIS M,AHMAD F (k, s)-Riemann-Liouville fractional integral and applications. Hacettepe Journal of Mathematics and Statistics. 2016; 45(1): 77 - 89.
Vancouver	Sarikaya M,DAHMANI Z,KIRIS M,AHMAD F (k, s)-Riemann-Liouville fractional integral and applications. Hacettepe Journal of Mathematics and Statistics. 2016; 45(1): 77 - 89.
IEEE	Sarikaya M,DAHMANI Z,KIRIS M,AHMAD F "(k, s)-Riemann-Liouville fractional integral and applications." Hacettepe Journal of Mathematics and Statistics, 45, ss.77 - 89, 2016.
ISNAD	Sarikaya, Mehmet vd. "(k, s)-Riemann-Liouville fractional integral and applications". Hacettepe Journal of Mathematics and Statistics 45/1 (2016), 77-89.