On fractional derivatives with generalized Mittag-Leffler kernels
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Abstract
Fractional derivatives with three parameter generalized Mittag-Leffler kernels and their properties are studied. The corresponding integral operators are obtained with the help of Laplace transforms. The action of the presented fractional integrals on the Caputo and Riemann type derivatives with three parameter Mittag-Leffler kernels is analyzed. Integration by parts formulas in the sense of Riemann and Caputo are proved and then used to formulate the fractional Euler-Lagrange equations with an illustrative example. Certain nonconstant functions whose fractional derivatives are zero are determined as well.
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Fractional Derivatives With Generalized Mittag-Leffler Kernels, Generalized Mittag-Leffler Function, Laplace Transform Convolution, Euler-Lagrange Equation, Integration By Parts, Euler–Lagrange Equation, Fractional Differential Equations, Laplace transform, Action (physics), Euler–Lagrange equation, Integration by parts, Theory and Applications of Fractional Differential Equations, Mathematical analysis, Quantum mechanics, Differential equation, Fractional derivatives with generalized Mittag-Leffler kernels, QA1-939, FOS: Mathematics, Biology, Anomalous Diffusion Modeling and Analysis, Mittag-Leffler function, Ecology, Applied Mathematics, Physics, Fractional calculus, Pure mathematics, Applied mathematics, Nonlocal Partial Differential Equations and Boundary Value Problems, Fractional Derivatives, Laplace transform convolution, Modeling and Simulation, FOS: Biological sciences, Physical Sciences, Generalized Mittag-Leffler function, Fractional Calculus, Type (biology), Mathematics, Ordinary differential equation, fractional derivatives, generalized Mittag-Leffler kernels, Mittag-Leffler functions and generalizations, generalized Mittag-Leffler function, Fractional derivatives and integrals, integration by parts, Euler-Lagrange equation
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Abdeljawad, Thabet; Baleanu, Dumitru (2018). On fractional derivatives with generalized Mittag-Leffler kernels, Advances in Difference Equations.
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65
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2018
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1
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