Dumitru Băleanu

An existence result for a superlinear fractional differential equation

Abstract We establish the existence and uniqueness of solution for the boundary value problem 0 D t α ( x ′ ) + a ( t ) x λ = 0 , t > 0 , x ′ ( 0 ) = 0 , lim t → + ∞ x ( t ) = 1 , where 0 D t α designates the Riemann–Liouville derivative of order α ∈ ( 0 , 1 ) and λ > 1 . Our result might be useful for establishing a non-integer variant of the Atkinson classical theorem on the oscillation of Emden–Fowler equations.

On Lp-solutions for a class of sequential fractional differential equations

Abstract Under some simple conditions on the coefficient a ( t ), we establish that the initial value problem 0 D t α x ′ + a ( t ) x = 0 , t > 0 , lim t ↘ 0 [ t 1 - α x ( t ) ] = 0 has no solution in L p ( ( 1 , + ∞ ) , R ) , where p - 1 p > α > 1 p and 0 D t α designates the Riemann–Liouville derivative of order α . Our result might be useful for developing a non-integer variant of H. Weyl’s limit-circle/limit-point classification of differential equations.

Asymptotically Linear Solutions for Some Linear Fractional Differential Equations

We establish here that under some simple restrictions on the functional coefficient the fractional differential equation , has a solution expressible as for , where designates the Riemann-Liouville derivative of order and .

Uniqueness and existence of positive solutions for a multi-point boundary value problem of singular fractional differential equations

In this paper, we study the uniqueness of a positive solution for the singular nonlinear fractional differential equation boundary value problem D0+αu(t)+f(t,u(t))=0, 0<t<1, u(0)=0, u(1)=aDα−12u(t)|t=ξ, where 1<α≤2 is a real number, D0+α is the standard Riemann-Liouville differentiation and f:(0,1]×[0,+∞)→[0,+∞), with limt→0+f(t,⋅)=+∞. Our analysis relies on a fixed-point theorem in partially ordered set. As an application, an example is presented to illustrate the main result.MSC:26A33, 34B15, 34K37.

On the asymptotic integration of a class of sublinear fractional differential equations

We estimate the growth in time of the solutions to a class of nonlinear fractional differential equations

New method and treatment technique applied to interband transition in GaAs1−xPx ternary alloys

D_{0+}^{\alpha}(x-x_0) =f(t,x)

On a fractional differential equation with infinitely many solutions

which includes

On the solution set for a class of sequential fractional differential equations

D_{0+}^{\alpha}(x-x_0) =H(t)x^{\lambda}

Asymptotic integration of some nonlinear differential equations with fractional time derivative

with

A uniqueness criterion for fractional differential equations with Caputo derivative

\lambda\in(0,1)