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Fractional Cauchy problems for infinite interval case
Fractional Ostrowski-Sugeno Fuzzy univariate inequalities
Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA |
Here we present fractional univariate Ostrowski-Sugeno Fuzzy type inequalities. These are of Ostrowski-like inequalities in the setting of Sugeno fuzzy integral and its special-particular properties. In a fractional environment, they give tight upper bounds to the deviation of a function from its Sugeno-fuzzy averages. The fractional derivatives we use are of Canavati and Caputo types. This work is greatly inspired by [
References:
| [1] |
G. A. Anastassiou, Fractional Differentiation Inequalities, Springer, Dordrecht, 2009.
doi: 10.1007/978-0-387-98128-4. |
| [2] |
G. A. Anastassiou, Advances on Fractional Inequalities, SpringerBriefs in Mathematics, Springer, New York, 2011.
doi: 10.1007/978-1-4614-0703-4. |
| [3] |
G. A. Anastassiou, Intelligent Mathematics: Computational Analysis, Intelligent Systems Reference Library, 5. Springer-Verlag, Berlin, 2011.
doi: 10.1007/978-3-642-17098-0. |
| [4] |
G. A. Anastassiou, Intelligent Comparisons: Analytic Inequalities, Studies in Computational Intelligence, 609. Springer, Cham, 2016.
doi: 10.1007/978-3-319-21121-3. |
| [5] |
M. Boczek and M. Kaluszka,
On the Minkowaki-Hölder type inequalities for generalized Sugeno integrals with an application, Kybernetika (Prague), 52 (2016), 329-347.
doi: 10.14736/kyb-2016-3-0329. |
| [6] |
J. A. Canavati,
The Riemann-Liouville integral, Nieuw Arch. Wisk., 5 (1987), 53-75.
|
| [7] |
K. Diethelm, The Analysis of Fractional Differential Equations, An application-oriented exposition using differential operators of Caputo type, Lecture Notes in Mathematics, 2004. Springer-Verlag, Berlin, 2010.
doi: 10.1007/978-3-642-14574-2. |
| [8] |
A. Ostrowski,
Über die Absolutabweichung einer differentiebaren Funktion von ihrem Integralmittelwert, (German) Comment. Math. Helv., 10 (1938), 226-227.
doi: 10.1007/BF01214290. |
| [9] |
E. Pap, Null-Additive Set functions, Mathematics and its Applications, 337, Kluwer Academic Publishers Group, Dordrecht; Ister Science, Bratislava, 1995. |
| [10] |
D. Ralescu and G. Adams,
The fuzzy integral, J. Math. Anal. Appl., 75 (1980), 562-570.
doi: 10.1016/0022-247X(80)90101-8. |
| [11] |
M. Sugeno, Theory of Fuzzy Integrals and Its Applications[J], PhD thesis, Tokyo Institute of Technology, 1974. |
| [12] |
Z. Wang and G. J. Klir, Fuzzy Measure Theory, Plenum Press, New York, 1992.
doi: 10.1007/978-1-4757-5303-5.
|
show all references
References:
| [1] |
G. A. Anastassiou, Fractional Differentiation Inequalities, Springer, Dordrecht, 2009.
doi: 10.1007/978-0-387-98128-4. |
| [2] |
G. A. Anastassiou, Advances on Fractional Inequalities, SpringerBriefs in Mathematics, Springer, New York, 2011.
doi: 10.1007/978-1-4614-0703-4. |
| [3] |
G. A. Anastassiou, Intelligent Mathematics: Computational Analysis, Intelligent Systems Reference Library, 5. Springer-Verlag, Berlin, 2011.
doi: 10.1007/978-3-642-17098-0. |
| [4] |
G. A. Anastassiou, Intelligent Comparisons: Analytic Inequalities, Studies in Computational Intelligence, 609. Springer, Cham, 2016.
doi: 10.1007/978-3-319-21121-3. |
| [5] |
M. Boczek and M. Kaluszka,
On the Minkowaki-Hölder type inequalities for generalized Sugeno integrals with an application, Kybernetika (Prague), 52 (2016), 329-347.
doi: 10.14736/kyb-2016-3-0329. |
| [6] |
J. A. Canavati,
The Riemann-Liouville integral, Nieuw Arch. Wisk., 5 (1987), 53-75.
|
| [7] |
K. Diethelm, The Analysis of Fractional Differential Equations, An application-oriented exposition using differential operators of Caputo type, Lecture Notes in Mathematics, 2004. Springer-Verlag, Berlin, 2010.
doi: 10.1007/978-3-642-14574-2. |
| [8] |
A. Ostrowski,
Über die Absolutabweichung einer differentiebaren Funktion von ihrem Integralmittelwert, (German) Comment. Math. Helv., 10 (1938), 226-227.
doi: 10.1007/BF01214290. |
| [9] |
E. Pap, Null-Additive Set functions, Mathematics and its Applications, 337, Kluwer Academic Publishers Group, Dordrecht; Ister Science, Bratislava, 1995. |
| [10] |
D. Ralescu and G. Adams,
The fuzzy integral, J. Math. Anal. Appl., 75 (1980), 562-570.
doi: 10.1016/0022-247X(80)90101-8. |
| [11] |
M. Sugeno, Theory of Fuzzy Integrals and Its Applications[J], PhD thesis, Tokyo Institute of Technology, 1974. |
| [12] |
Z. Wang and G. J. Klir, Fuzzy Measure Theory, Plenum Press, New York, 1992.
doi: 10.1007/978-1-4757-5303-5.
|
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