Lower-order Fractional Derivatives Research Articles

Uniqueness results for fully anti-periodic fractional boundary value problems with nonlinearity depending on lower-order derivatives

We investigate the uniqueness of solutions for fully anti-periodic fractional boundary value problems of order 2 < q ≤ 3 with nonlinearity depending on lower-order fractional derivatives. Our results are based on some standard fixed point theorems. The paper concludes with illustrative examples. MSC: 34A12; 34A40

Existence of positive solutions for a fractional boundary value problem with lower-order fractional derivative dependence on the half-line

Existence of positive solutions for a fractional boundary value problem with lower-order fractional derivative dependence on the half-line

Separated boundary value problem for fractional differential equations depending on lower-order derivative

We study a new class of boundary value problems of nonlinear fractional differential equations whose nonlinear term depends on a lower-order fractional derivative with fractional separated boundary conditions. Some existence and uniqueness results are obtained by using standard fixed point theorems. Examples are given to illustrate the results.

Anti-periodic fractional boundary value problems with nonlinear term depending on lower order derivative

Abstract This paper studies a new class of anti-periodic boundary value problems of fractional differential equations with nonlinear term depending on lower order fractional derivative. Some existence and uniqueness results are obtained by applying some standard fixed point principles. Several examples are given to illustrate the results.

Spatially fractional-order viscoelasticity, non-locality, and a new kind of anisotropy

A class of non-local viscoelastic equations of motion including equations of fractional order with respect to the spatial variables is studied. It is shown that space-fractional equations of motion of an order strictly less than 2 allow for a new kind of anisotropy, associated with azimuthal dependence of non-local interactions between stress and strain at different material points. Constitutive equations of such viscoelastic media are determined. Relaxation effects are additionally accounted for by replacing second-order time derivatives by lower-order fractional derivatives. Explicit fundamental solutions of the Cauchy problem for scalar equations with isotropic and anisotropic non-locality are constructed. For some particular choices of the parameters, numerical solutions are constructed.