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Opial-type inequalities for conformable fractional integrals

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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
Rocznik
Strony
155--163
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
  • Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey
  • 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
bwmeta1.element.baztech-619d32c6-a964-4bc6-bed4-d9c509f7940c
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