Abstract
In this paper, we introduce stochastic g-fractional integrals of order \( \alpha \), containing stochastic fractional integrals (Hafiz in Stoch Anal Appl 22:507–523, 2004), stochastic integral (Shaked and Shanthikumar in Adv Appl Prob 20:427–446, 1988) and stochastic pseudo integrals (Agahi in Stat Probab Lett 124:41–48, 2017). We determine the upper and lower bounds of stochastic g-fractional integrals for convex stochastic processes, generalizing some previous results in Kotrys (Aequat Math 83:143–151, 2012), Agahi (Aequat Math 90:765–772, 2016; 2017) and Agahi and Babakhani (Aequat Math 90:1035–1043, 2016).
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References
Agahi, H., Yadollahzadeh, M.: On stochastic pseudo-integrals with applications. Stat. Probab. Lett. 124, 41–48 (2017)
Agahi, H.: Refinements of mean-square stochastic integral inequalities on convex stochastic processes. Aequat. Math. 90, 765–772 (2016)
Agahi, H., Babakhani, A.: On fractional stochastic inequalities related to Hermite–Hadamard and Jensen types for convex stochastic processes. Aequat. Math. 90, 1035–1043 (2016)
Hafiz, F.M.: The fractional calculus for some stochastic processes. Stoch. Anal. Appl. 22, 507–523 (2004)
Hosseini, M., Babakhani, A., Agahi, H., Rasouli, S.H.: On pseudo-fractional integral inequalities related to Hermite–Hadamard type. Soft. Comput. 20(7), 2521–2529 (2016)
Kotrys, D.: Hermite-Hadamard inequality for convex stochastic processes. Aequat. Math. 83, 143–151 (2012)
Kotrys, D.: Remarks on strongly convex stochastic processes. Aequat. Math. 86, 91–98 (2013)
Kuich, W.: Semirings. Languages. Springer, Berlin (1986)
Mesiar, R., Pap, E.: Idempotent integral as limit of \(g\)-integrals. Fuzzy Sets Syst. 102, 385–392 (1999)
Nikodem, K.: On convex stochastic processes. Aequat. Math. 20, 184–197 (1980)
Pap, E.: An integral generated by decomposable measure. Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 20(1), 135–144 (1990)
Pap, E.: \(g\)-calculus. Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat 23(1), 145–156 (1993)
Pap, E.: Applications of the generated pseudo-analysis on nonlinear partial differential equations. In: Litvinov, G.L., Maslov, V.P. (Eds.), Proceedings of the Conference on Idempotent Mathematics and Mathematical Physics, Contemporary Mathematics, vol. 377, pp. 239–259. American Mathematical Society (2005)
Pap, E., Štrboja, M., Rudas, I.: Pseudo-\(L^{p}\) space and convergence. Fuzzy Sets Syst. 238, 113–128 (2014)
Shaked, M., Shanthikumar, J.G.: Stochastic convexity and its applications. Adv. Appl. Prob. 20, 427–446 (1988)
Skowroński, A.: On some properties of J-convex stochastic processes. Aequat. Math. 44, 249–258 (1992)
Sobczyk, K.: Stochastic differential equations with applications to physics and engineering. Kluwer, Dordrecht (1991)
Acknowledgements
The authors are very grateful to the anonymous reviewers for their suggestions. Hamzeh Agahi was supported by Babol Noshirvani University of Technology with Grant program No. BNUT/392100/98.
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Agahi, H., Karamali, G. & Yadollahzadeh, M. Stochastic g-Fractional Integrals and their Bounds for Convex Stochastic Processes. Results Math 74, 189 (2019). https://doi.org/10.1007/s00025-019-1112-x
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DOI: https://doi.org/10.1007/s00025-019-1112-x
Keywords
- Stochastic integral
- stochastic fractional integrals
- convex stochastic processes
- stochastic pseudo-fractional integrals
- fractional stochastic inequalities