ON THE GENERALIZED WEIGHTED CAPUTO-TYPE DIFFERENTIAL OPERATOR

Jian-Gen Liu, Xiao-Jun Yang, Yi-Ying Feng and Lu-Lu Geng
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Jian-Gen Liu: School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China†State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China
Xiao-Jun Yang: School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China†State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China‡School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China
Yi-Ying Feng: ��State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China‡School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China
Lu-Lu Geng: School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China†State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-7

Abstract: In this paper, we defined a generalized weighted Caputo-type differential operator. Then, it can express as a convergent series through the Riemann–Liouville integral. At the same time, by solving related linear differential equation, we can construct the generalized weighted Caputo-type integral operator. Lastly, some theorems and properties of these considered operators were also studied.

Keywords: Generalized Weighted Caputo-Type Differential Operator; Generalized Weighted Caputo-Type Integral Operator; Riemann–Liouville Integral (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22500323

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