Baleanu, DumitruIbrahim, Rabha W.2024-04-032025-09-182024-04-032025-09-182021Rabha, W. Ibrahim; Baleanu, D. (2021). "Generalized Quantum Integro-Differential Fractional Operator with Application of 2D-Shallow Water Equation in a Complex Domain", Axioms, Vol.10, No.342, pp. 1-12.2075-1680https://doi.org/10.3390/axioms10040342https://hdl.handle.net/20.500.12416/12092Ibrahim, Rabha W./0000-0001-9341-025XIn this paper, we aim to generalize a fractional integro-differential operator in the open unit disk utilizing Jackson calculus (quantum calculus or q-calculus). Next, by consuming the generalized operator to define a formula of normalized analytic functions, we present a set of integral inequalities using the concepts of subordination and superordination. In addition, as an application, we determine the maximum and minimum solutions of the extended fractional 2D-shallow water equation in a complex domain.eninfo:eu-repo/semantics/openAccessQuantum CalculusFractional CalculusAnalytic FunctionSubordinationUnivalent FunctionOpen Unit DiskDifferential OperatorConvolution OperatorArticle10.3390/axioms100403422-s2.0-85121616501