On fractional derivatives with exponential kernel and their discrete versions

By Thabet Abdeljawad, Dumitru Băleanu. 2016

215 citations recorded by the source corpus.

In this manuscript we define the right fractional derivative and its corresponding right fractional integral with exponential kernel. Then, we provide the integration by parts formula and we use $Q-$operator to confirm our results. The related Euler-Lagrange equations were obtained and one example is analyzed. Moreover, we formulate and discus the discrete counterparts of our results.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/262d65af32ec0e5946bfe0c4f225aeac318b745c

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In Applied Mathematics

In Modeling and Simulation

Citations in the corpus

Arbitrary Order Fractional Difference Operators with Discrete Exponential Kernels and Applications (2017, methodology): “Then, the authors in [7] defined the left and right fractional derivatives with exponential kernel in the Riemann sense and formulated the right fractional derivatives in the sense of Caputo-Fabrizio with complete investigation to the correspondent fractional integrals and all the discrete versions ”
Fractional Integral Inequalities via Atangana-Baleanu Operators for Convex and Concave Functions (2021, background): “[4] Let f ∈ H(1)(0, θ2), θ2 > θ1, α ∈ [0, 1] then, the definition of the left and right side of Caputo-Fabrizio fractional integral is:”
Fundamental solutions of anomalous diffusion equations with the decay exponential kernel (2019, unknown): “H RRI n,μ a+ f (t) = t ∫ a (τ − t)n−2E−1 1,n−1 (−μ (τ − t)) f (τ)dτ, (16)”