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Abstrakty
In this paper, we establish the Opial-type inequalities for a conformable fractional integral and give some results in special cases of α. The results presented here would provide generalizations of those given in earlier works.
Wydawca
Czasopismo
Rocznik
Tom
Strony
155--163
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
autor
- Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey
autor
- Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey
Bibliografia
- [1] T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math. 279 (2015), 57-66.
- [2] D. R. Anderson, Taylor’s formula and integral inequalities for conformable fractional derivatives, in: Contributions in Mathematics and Engineering, Springer, Cham (2016), 25-43.
- [3] W. S. Cheung, Some new Opial-type inequalities, Mathematika 37 (1990), no. 1, 136-142.
- [4] W. S. Cheung, Some generalized Opial-type inequalities, J. Math. Anal. Appl. 162 (1991), no. 2, 317-321.
- [5] M. A. Hammad and R. Khalil, Abel’s formula and wronskian for conformable fractional differential equations, Int. J. Differ. Equ. Appl. 13 (2014), no. 3, 177-183.
- [6] M. A. Hammad and R. Khalil, Conformable fractional heat differential equations, Int. J. Pure Appl. Math. 94 (2014), no. 2, 215-221.
- [7] O. S. Iyiola and E. R. Nwaeze, Some new results on the new conformable fractional calculus with application using D’Alambert approach, Progr. Fract. Differ. Appl. 2 (2016), no. 2, 115-122.
- [8] R. Khalil, M. Al Horani, A. Yousef and M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math. 264 (2014), 65-70.
- [9] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Math. Stud. 204, Elsevier Science B.V., Amsterdam, 2006.
- [10] Z. Opial, Sur une inégalité, Ann. Polon. Math. 8 (1960), 29-32.
- [11] B. G. Pachpatte, On Opial-type integral inequalities, J. Math. Anal. Appl. 120 (1986), no. 2, 547-556.
- [12] B. G. Pachpatte, Some inequalities similar to Opial’s inequality, Demonstratio Math. 26 (1993), no. 3-4, 643-647.
- [13] B. G. Pachpatte, On some inequalities of the Weyl type, An. Ştiinț. Univ. Al. I. Cuza Iaşi Secț. I A Mat. 40 (1994), no. 1, 89-95.
- [14] B. G. Pachpatte, A note on some new Opial type integral inequalities, Octogon Math. Mag. 7 (1999), no. 1, 80-84.
- [15] H. M. Srivastava, K.-L. Tseng, S.-J. Tseng and J.-C. Lo, Some weighted Opial-type inequalities on time scales, Taiwanese J. Math. 14 (2010), no. 1, 107-122.
- [16] J. Traple, On a boundary value problem for systems of ordinary differential equations of second order, Zeszyty Nauk. Uniw. Jagielloń. Prace Mat. (1971), no. 15, 159-168.
- [17] C.-J. Zhao and W.-S. Cheung, On Opial-type integral inequalities and applications, Math. Inequal. Appl. 17 (2014), no. 1, 223-232.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
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