Jorge Losada

Three-Point Boundary Value Problems for Conformable Fractional Differential Equations

We study a fractional differential equation using a recent novel concept of fractional derivative with initial and three-point boundary conditions. We first obtain Greens function for the linear problem and then we study the nonlinear differential equation.

On Fractional Derivatives and Primitives of Periodic Functions

We prove that the fractional derivative or the fractional primitive of a -periodic function cannot be a -periodic function, for any period , with the exception of the zero function.

On the attractivity of solutions for a class of multi-term fractional functional differential equations

In this paper, we present some alternative results concerning with the existence and attractivity dependence of solutions for a class of nonlinear fractional functional differential equations. In our consideration, we apply the well-known Schauder fixed point theorem in conjunction with the technique of measure of noncompactness. Moreover, we provide some examples to illustrate the effectiveness of the obtained results.

On Fractional Orthonormal Polynomials of a Discrete Variable

A fractional analogue of classical Gram or discrete Chebyshev polynomials is introduced. Basic properties as well as their relation with the fractional analogue of Legendre polynomials are presented.

On Some Fractional Pearson Equations

Abstract In this paper some fractional analogues of classical Pearson differential equations are explicitly solved. Limit transitions between the solutions are analyzed, providing a generalization of well-known transitions between the beta and gamma, and between the gamma and normal distributions. Finally, quasi-polynomials orthogonal with respect to these fractional analogues of the classical distributions are introduced, and some conjectures about their zeros are posed.

On quasi-periodicity properties of fractional integrals and fractional derivatives of periodic functions

ABSTRACT This paper is devoted to the study of quasi-periodic properties of fractional order integrals and derivatives of periodic functions. Considering Riemann–Liouville and Caputo definitions, we discuss when the fractional derivative and when the fractional integral of a certain class of periodic functions satisfies particular properties. We study concepts close to the well known idea of periodic function, such as S-asymptotically periodic, asymptotically periodic or almost periodic function. Boundedness of fractional derivative and fractional integral of a periodic function is also studied.

On Antiperiodic Nonlocal Three-Point Boundary Value Problems for Nonlinear Fractional Differential Equations

We introduce boundary value conditions involving antiperiodic and nonlocal three-point boundary conditions. We solve a nonlinear fractional differential equation supplemented with those conditions. We obtain some existence results for the given problem by applying some standard tools of fixed point theory. These results are well illustrated with the aid of examples.