Generalized Quantum Integro-Differential Fractional Operator With Application of 2d-Shallow Water Equation in a Complex Domain
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Abstract
In 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.
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Ibrahim, Rabha W./0000-0001-9341-025X
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Keywords
Quantum Calculus, Fractional Calculus, Analytic Function, Subordination, Univalent Function, Open Unit Disk, Differential Operator, Convolution Operator, QA1-939, subordination, fractional calculus, quantum calculus, univalent function, quantum calculus; fractional calculus; analytic function; subordination; univalent function; open unit disk; differential operator; convolution operator, analytic function, open unit disk, Mathematics
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0101 mathematics, 01 natural sciences
Citation
Rabha, 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.
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10
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4
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342
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Scopus : 1
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