Fractional differential equation with the fuzzy initial condition.
Fractional differential equations in terms of comparison results and Lyapunov stability with initial time difference.
Fractional order impulsive partial hyperbolic differential inclusions with variable times
This paper deals with the existence of solutions to some classes of partial impulsive hyperbolic differential inclusions with variable times involving the Caputo fractional derivative. Our works will be considered by using the nonlinear alternative of Leray-Schauder type.
Fractional positive continuous-time linear systems and their reachability
A new class of fractional linear continuous-time linear systems described by state equations is introduced. The solution to the state equations is derived using the Laplace transform. Necessary and sufficient conditions are established for the internal and external positivity of fractional systems. Sufficient conditions are given for the reachability of fractional positive systems.
Fractional-order Bessel functions with various applications
We introduce fractional-order Bessel functions (FBFs) to obtain an approximate solution for various kinds of differential equations. Our main aim is to consider the new functions based on Bessel polynomials to the fractional calculus. To calculate derivatives and integrals, we use Caputo fractional derivatives and Riemann-Liouville fractional integral definitions. Then, operational matrices of fractional-order derivatives and integration for FBFs are derived. Also, we discuss an error estimate between...
Fractional-order variational calculus with generalized boundary conditions.
Frequency analysis of preconditioned waveform relaxation iterations
The error analysis of preconditioned waveform relaxation iterations for differential systems is presented. This analysis extends and refines previous results by Burrage, Jackiewicz, Nørsett and Renaut by incorporating all terms in the expansion of the error of waveform relaxation iterations in the Laplace transform domain. Lower bounds for the size of the window of rapid convergence are also obtained. The theory is illustrated for waveform relaxation methods applied to differential systems resulting...
Functional differential equations
The method of quasilinearization is a well-known technique for obtaining approximate solutions of nonlinear differential equations. In this paper we apply this technique to functional differential problems. It is shown that linear iterations converge to the unique solution and this convergence is superlinear.
Functional differential equations with pulses.
Functional differential inclusions with integral boundary conditions.
Functional evolution equations with nonconvex lower semicontinuous multivalued perturbations.
Functional viability theorems for differential inclusions with memory
Functional-differential equations with Riemann-Liouville integrals in the nonlinearities
A sufficient condition for the nonexistence of blowing-up solutions to evolution functional-differential equations in Banach spaces with the Riemann-Liouville integrals in their right-hand sides is proved. The linear part of such type of equations is an infinitesimal generator of a strongly continuous semigroup of linear bounded operators. The proof of the main result is based on a desingularization method applied by the author in his papers on integral inequalities with weakly singular kernels....
Functions of finite fractional variation and their applications to fractional impulsive equations
We introduce a notion of a function of finite fractional variation and characterize such functions together with their weak -additive fractional derivatives. Next, we use these functions to study differential equations of fractional order, containing a -additive term—we prove existence and uniqueness of a solution as well as derive a Cauchy formula for the solution. We apply these results to impulsive equations, i.e. equations containing the Dirac measures.
Functions without residue and a bilinear differential equation
Fundamental central dispersion in a simple system
Fundamental central dispersions in a double system
Fundamental central dispersions of the phase function with the final oscillation
Fundamental quadratic splines and applications
Fundamental theorems for linear measure differential equations.