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Numerical Approximations of Fractional Derivatives with Applications
Shakoor Pooseh, Ricardo Almeida, Delfim F. M. Torres
Two approximations, derived from continuous expansions of Riemann-Liouville fractional derivatives into series involving integer order derivatives, are studied. Using those series,…
Generalized Transversality Conditions in Fractional Calculus of Variations
Ricardo Almeida, Agnieszka B. Malinowska
Problems of calculus of variations with variable endpoints cannot be solved without transversality conditions. Here, we establish such type of conditions for fractional variational…
Discrete Direct Methods in the Fractional Calculus of Variations
Shakoor Pooseh, Ricardo Almeida, Delfim F. M. Torres
Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives…