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Fractional differential equations with mixed boundary conditions
Ricardo Almeida
In this paper, we discuss the existence and uniqueness of solutions of a boundary value problem for a fractional differential equation of order , involving a general for…
A Gronwall inequality for a general Caputo fractional operator
Ricardo Almeida
In this paper we present a new type of fractional operator, which is a generalization of the Caputo and Caputo--Hadamard fractional derivative operators. We study some properties o…
A remark on local fractional calculus and ordinary derivatives
Ricardo Almeida, Malgorzata Guzowska, Tatiana Odzijewicz
In this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some…
A Caputo fractional derivative of a function with respect to another function
Ricardo Almeida
In this paper we consider a Caputo type fractional derivative with respect to another function. Some properties, like the semigroup law, a relationship between the fractional deriv…
Fractional differential equations with dependence on the Caputo-Katugampola derivative
Ricardo Almeida, Agnieszka B. Malinowska, Tatiana Odzijewicz
In this paper we present a new type of fractional operator, the Caputo-Katugampola derivative. The Caputo and the Caputo-Hadamard fractional derivatives are special cases of this n…
Fractional variational problems depending on indefinite integrals and with delay
Ricardo Almeida
The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals an…