Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel

By Thabet Abdeljawad, Dumitru Băleanu. 2016

307 citations recorded by the source corpus.

In this manuscript we define the right fractional derivative and its corresponding right fractional integral for the recently introduced nonlocal fractional derivative with Mittag-Leffler kernel. Then, we obtain the related integration by parts formula. We use the $Q-$operator to confirm our results. The corresponding Euler-Lagrange equations are obtained and one illustrative example is discussed.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/ac95820c1e0291b0f2ae2fcae81d8a6611f6d8dc

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Analysis of some generalized ABC – Fractional logistic models (2019, background): “After this derivative had been proposed, most of the works treated by the traditional fractional derivative were reconsidered by the new approach [19, 20].”
Integral inequalities for a fractional operator of a function with respect to another function with nonsingular kernel (2020, background): “Also, they have their own properties consistent with those of the ML functions [5, 15, 18, 27].”
New aspects of time fractional optimal control problems within operators with nonsingular kernel (2020, background): “Moreover, fractional calculus in continuous and discrete cases [33, 5, 4, 11, 7, 6, 1, 9, 2, 3] have been applied to physics [26], bioengineering [42], optics [24], fluid flow [21], energy systems [37] and biology [56, 54, 50, 47, 31, 30].”
Generalized fractional derivatives and Laplace transform (2020, background): “The question arises here is the possibility of developing a new integral transform that can be easily applied to solve dynamical systems in the frame of fractional operators with nonsingular kernels [8], [3], [4].”
On some new properties of fractional derivatives with Mittag-Leffler kernel (2017, methodology): “Applications of the new AB formula have been explored in fields as diverse as chaos theory [5], heat transfer [9], and variational problems [2].”
Analysis and numerical computations of the fractional regularized long‐wave equation with damping term (2020, unknown): “φ(φ) = Ωφξξζ + Ωξφξζ + φξξ − φξ − φφξ (16)”