Mathematics · 2019 · 106 citations · 27 references
Natural SciencesMathematicsInsurance OperationsNumber TheoryOptimizationIntegral EquationsNumerical IntegrationProbability InequalitiesSpecial FunctionsApproximation Properties
In this article, we define a new fractional technique which is known as generalized proportional fractional (GPF) integral in the sense of another function Ψ . The authors prove several inequalities for newly defined GPF-integral with respect to another function Ψ . Our consequences will give noted outcomes for a suitable variation to the GPF-integral in the sense of another function Ψ and the proportionality index ς . Furthermore, we present the application of the novel operator with several integral inequalities. A few new properties are exhibited, and the numerical approximation of these new operators is introduced with certain utilities to real-world problems.
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A new definition of fractional derivative
Roshdi Khalil, Mohammed Al Horani, A. Yousef et al. · Journal of Computational and Applied Mathematics · 2014 · 3.4K citations