On the existence of mild solutions to some semilinear fractional integro-differential equations.
On the selection and meaning of variable order operators for dynamic modeling.
On the stability of a fractional-order differential equation with nonlocal initial condition.
On type of periodicity and ergodicity to a class of fractional order differential equations.
Oscillation of impulsive conformable fractional differential equations
In this paper, we investigate oscillation results for the solutions of impulsive conformable fractional differential equations of the form tkDαpttkDαxt+rtxt+qtxt=0,t≥t0,t≠tk,xtk+=akx(tk−),tkDαxtk+=bktk−1Dαx(tk−),k=1,2,…. Some new oscillation results are obtained by using the equivalence transformation and the associated Riccati techniques.
Pointwise completeness and pointwise degeneracy of positive fractional descriptor continuous-time linear systems with regular pencils
Pointwise completeness and pointwise degeneracy of positive fractional descriptor continuous-time linear systems with regular pencils are addressed. Conditions for pointwise completeness and pointwise degeneracy of the systems are established and illustrated by an example.
Positive solution of singular boundary value problem for a nonlinear fractional differential equation.
Positive solution to nonzero boundary values problem for a coupled system of nonlinear fractional differential equations.
Positive solutions for a system of fractional boundary value problems
We investigate the existence and multiplicity of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with nonnegative nonlinearities which can be nonsingular or singular functions, subject to multi-point boundary conditions that contain fractional derivatives.
Positive solutions for multipoint boundary value problem of fractional differential equations.
Positive solutions of a boundary value problem for a nonlinear fractional differential equation.
Positive solutions of -point boundary value problems for fractional differential equations.
Positive solutions to boundary value problems of nonlinear fractional differential equations.
Positive solutions to nonlinear higher-order nonlocal boundary value problems for fractional differential equations.
Positive stable realizations of fractional continuous-time linear systems
Conditions for the existence of positive stable realizations with system Metzler matrices for fractional continuous-time linear systems are established. A procedure based on the Gilbert method for computation of positive stable realizations of proper transfer matrices is proposed. It is shown that linear minimum-phase systems with real negative poles and zeros always have positive stable realizations.
Relative controllability of nonlinear fractional delay integrodifferential systems with multiple delays in control
This paper describes the controllability of nonlinear fractional delay integrodifferential systems with multiple delays in control. Necessary and sufficient conditions for the controllability criteria for linear fractional delay system are established. Further sufficient conditions for the controllability of nonlinear fractional delay integrodifferential system are obtained by using fixed point arguments. Examples are provided to illustrate the results.
Robust stabilization of fractional-order systems with interval uncertainties via fractional-order controllers.
Singular fractional linear systems and electrical circuits
A new class of singular fractional linear systems and electrical circuits is introduced. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and the Laplace transformation, the solution to the state equation of singular fractional linear systems is derived. It is shown that every electrical circuit is a singular fractional system if it contains at least one mesh consisting of branches only with an ideal supercapacitor and voltage sources or at least...
Singular positone and semipositone boundary value problems of nonlinear fractional differential equations.
Solution to the linear fractional differential equation using Adomian decomposition method.