New generalization of reverse Minkowski's inequality for fractional integral
Yıl 2021,
, 72 - 81, 31.03.2021
Tariq A. Aljaaidi
,
Deepak Pachpatte
Öz
In this research, we introduce some new fractional integral inequalities of Minkowski’s type by using Riemann-Liouville fractional
integral operator. We replace the constants that appear on Minkowski’s inequality by two positive functions. Further, we
establish some new fractional inequalities related to the reverse Minkowski type inequalities via Riemann-Liouville fractional
integral. Using this fractional integral operator, some special cases of reverse Minkowski type are also discussed.
Kaynakça
- [1] M.S. Abdo, K. shah, S.K. Panchal, H.A. Wahash, Existence and Ulam stability results of a coupled system for terminal
value problems involving -Hilfer fractional operator, Adv. Di er. Equ., 2020(1), 1-21.
- [2] M.S. Abdo, T.Abdeljawad, S. M. Ali, K. shah, F. Jarad, Existence of positive solutions for weighted fractional order
differential equations, Chaos Solitons Fractals 141, (2020), 110341. https://doi.org/10.1016/j.chaos.2020.110341
- [3] T.A. Aljaaidi, D.B. Pachpatte, Some Gruss-type Inequalities Using Generalized Katugampola Fractional Integral, AIMS
Mathematics, 5(2), (2020), 1011-1024. doi: 10.3934/math.2020070
- [4] T.A. Aljaaidi, D.B. Pachpatte, The Minkowski's Inequalities via ψ-Riemann-Liouville fractional Integral Operators, Rend.
Circ. Mat. Palermo, ii. ser. (2020). https://doi.org/10.1007/s12215-020-00539-w
- [5] G.A. Anastassiou, Fractional Differentiation Inequalities, Springer, Dordrecht, The Netherlands, (2010).
- [6] L. Bougoffa, On Minkowski and Hardy integral inequalities, Journal of Inequalities in Pure and Applied Mathematics, 7
(2), (2006), 1-3.
- [7] V.L. Chinchane, D.B. Pachpatte, New fractional inequalities involving Saigo fractional integral operator, Math. Sci. Lett.,
3 (3), (2014), 133-139.
- [8] V. L. Chinchane, D. B. Pachpatte, New fractional inequalities via Hadamard fractional integral, Internat. J. Functional
Analysis and Application, 5 (3), (2013), 165-176. http://dx.doi.org/10.12785/msl/030301
- [9] Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal., 1
(1), (2010), 51-58.
- [10] R. Herrmann, Fractional Calculus: An Introduction for Physicists, World Scientifc, Singapore (2011).
- [11] E. Kreyszig, Introductory Functional Analysis with Applications, vol 1, Wiley, New York, (1989).
- [12] H. Khan, T. Abdeljawad, C. Tunç, A. Alkhazzan, A. Khan, Minkowski's inequality for the AB-fractional integral operator,
J. Inequal. Appl., (96), (2019). https://doi.org/10.1186/s13660-019-2045-3
- [13] A.A. Kilbas, H.M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Di?erential Equations, North-Holland
Mathematics Studies, Elsevier, Amsterdam, (2006).
- [14] S. Mubeen, S. Habib, M.N. Naeem, The Minkowski inequality involving generalized k-fractional conformable integral, J.
Inequal. Appl., (81), (2019), (Online). https://doi.org/10.1186/s13660-019-2040-8
- [15] G. Rahman, A. Khan, T. Abdeljawad, K.S. Nisar, The Minkowski inequalities via generalized proportional fractional
integral operators, Advances in Di?erence Equations, (287), (2019). https://doi.org/10.1186/s13662-019-2229-7
- [16] E. Set, M. Ozdemir, S. Dragomir, On the Hermite-Hadamard inequality and other integral inequalities involving two
functions, J. Inequal. Appl., (2010), (online). https://doi.org/10.1155/2010/148102
- [17] J. Sousa, D. S. Oliveira, E. Capelas de Oliveira, Gruss-Type Inequalities by Means of Generalized Fractional Integrals,
Bull. Braz. Math. Soc., 50 (4), (2019) (online). https://doi.org/10.1007/s00574-019-00138-z
- [18] W.T. Sulaiman, Reverses of Minkowski's, Hölder's, and Hardy's integral inequalities, Int. J. Mod. Math. Sci., 1 (1), (2012),
14-24.
- [19] S. Taf, K. Brahim, Some new results using Hadamard fractional integral, Int. J. Nonlinear Anal. Appl., 7 (1) (2015),
103-109.
- [20] F. Usta, H. Budak, F. Ertu gral, M.Z. Sarikaya, The Minkowski's inequalities utilizing newly defined generalized fractional
integral operators, Commun. Fac. Sci. Univ. Ank. Sér. A1 Math. Stat., 68 (1), (2019), 686-701.
- [21] J. Vanterler da, C. Sousa, E. Capelas de Oliveira, The Minkowski's inequality by means of a generalized fractional integral,
AIMS Ser. Appl. Math. 3 (1), (2018), 131-147.
Yıl 2021,
, 72 - 81, 31.03.2021
Tariq A. Aljaaidi
,
Deepak Pachpatte
Kaynakça
- [1] M.S. Abdo, K. shah, S.K. Panchal, H.A. Wahash, Existence and Ulam stability results of a coupled system for terminal
value problems involving -Hilfer fractional operator, Adv. Di er. Equ., 2020(1), 1-21.
- [2] M.S. Abdo, T.Abdeljawad, S. M. Ali, K. shah, F. Jarad, Existence of positive solutions for weighted fractional order
differential equations, Chaos Solitons Fractals 141, (2020), 110341. https://doi.org/10.1016/j.chaos.2020.110341
- [3] T.A. Aljaaidi, D.B. Pachpatte, Some Gruss-type Inequalities Using Generalized Katugampola Fractional Integral, AIMS
Mathematics, 5(2), (2020), 1011-1024. doi: 10.3934/math.2020070
- [4] T.A. Aljaaidi, D.B. Pachpatte, The Minkowski's Inequalities via ψ-Riemann-Liouville fractional Integral Operators, Rend.
Circ. Mat. Palermo, ii. ser. (2020). https://doi.org/10.1007/s12215-020-00539-w
- [5] G.A. Anastassiou, Fractional Differentiation Inequalities, Springer, Dordrecht, The Netherlands, (2010).
- [6] L. Bougoffa, On Minkowski and Hardy integral inequalities, Journal of Inequalities in Pure and Applied Mathematics, 7
(2), (2006), 1-3.
- [7] V.L. Chinchane, D.B. Pachpatte, New fractional inequalities involving Saigo fractional integral operator, Math. Sci. Lett.,
3 (3), (2014), 133-139.
- [8] V. L. Chinchane, D. B. Pachpatte, New fractional inequalities via Hadamard fractional integral, Internat. J. Functional
Analysis and Application, 5 (3), (2013), 165-176. http://dx.doi.org/10.12785/msl/030301
- [9] Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal., 1
(1), (2010), 51-58.
- [10] R. Herrmann, Fractional Calculus: An Introduction for Physicists, World Scientifc, Singapore (2011).
- [11] E. Kreyszig, Introductory Functional Analysis with Applications, vol 1, Wiley, New York, (1989).
- [12] H. Khan, T. Abdeljawad, C. Tunç, A. Alkhazzan, A. Khan, Minkowski's inequality for the AB-fractional integral operator,
J. Inequal. Appl., (96), (2019). https://doi.org/10.1186/s13660-019-2045-3
- [13] A.A. Kilbas, H.M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Di?erential Equations, North-Holland
Mathematics Studies, Elsevier, Amsterdam, (2006).
- [14] S. Mubeen, S. Habib, M.N. Naeem, The Minkowski inequality involving generalized k-fractional conformable integral, J.
Inequal. Appl., (81), (2019), (Online). https://doi.org/10.1186/s13660-019-2040-8
- [15] G. Rahman, A. Khan, T. Abdeljawad, K.S. Nisar, The Minkowski inequalities via generalized proportional fractional
integral operators, Advances in Di?erence Equations, (287), (2019). https://doi.org/10.1186/s13662-019-2229-7
- [16] E. Set, M. Ozdemir, S. Dragomir, On the Hermite-Hadamard inequality and other integral inequalities involving two
functions, J. Inequal. Appl., (2010), (online). https://doi.org/10.1155/2010/148102
- [17] J. Sousa, D. S. Oliveira, E. Capelas de Oliveira, Gruss-Type Inequalities by Means of Generalized Fractional Integrals,
Bull. Braz. Math. Soc., 50 (4), (2019) (online). https://doi.org/10.1007/s00574-019-00138-z
- [18] W.T. Sulaiman, Reverses of Minkowski's, Hölder's, and Hardy's integral inequalities, Int. J. Mod. Math. Sci., 1 (1), (2012),
14-24.
- [19] S. Taf, K. Brahim, Some new results using Hadamard fractional integral, Int. J. Nonlinear Anal. Appl., 7 (1) (2015),
103-109.
- [20] F. Usta, H. Budak, F. Ertu gral, M.Z. Sarikaya, The Minkowski's inequalities utilizing newly defined generalized fractional
integral operators, Commun. Fac. Sci. Univ. Ank. Sér. A1 Math. Stat., 68 (1), (2019), 686-701.
- [21] J. Vanterler da, C. Sousa, E. Capelas de Oliveira, The Minkowski's inequality by means of a generalized fractional integral,
AIMS Ser. Appl. Math. 3 (1), (2018), 131-147.