Forewords : European Conference on Iteration Theory - ECIT 2010
Form of general pointwise transformations of linear differential equations
Formal adjoints of linear DAE operators and their role in optimal control.
Formally normal ordinary differential operators
Former super-irrécductibles des systèmes différentiels linéaires.
Formulas of variation for a solution of neutral differential equations with continuous initial condition.
Fourier multipliers for Hölder continuous functions and maximal regularity
Two operator-valued Fourier multiplier theorems for Hölder spaces are proved, one periodic, the other on the line. In contrast to the -situation they hold for arbitrary Banach spaces. As a consequence, maximal regularity in the sense of Hölder can be characterized by simple resolvent estimates of the underlying operator.
Fractal analysis of Hopf bifurcation for a class of completely integrable nonlinear Schrödinger Cauchy problems.
Fractional BVPs with strong time singularities and the limit properties of their solutions
In the first part, we investigate the singular BVP , u(0) = A, u(1) = B, c D α u(t)|t=0 = 0, where is a continuous operator, α ∈ (0, 1) and a < 0. Here, c D denotes the Caputo fractional derivative. The existence result is proved by the Leray-Schauder nonlinear alternative. The second part establishes the relations between solutions of the sequence of problems , u(0) = A, u(1) = B, where a < 0, 0 < β n ≤ α n < 1, limn→∞ β n = 1, and solutions of u″+(a/t)u′ = f(t, u, u′) satisfying...
Fractional differential equation with the fuzzy initial condition.
Fractional differential equations in terms of comparison results and Lyapunov stability with initial time difference.
Fractional evolution equations governed by coercive differential operators.
Fractional integro-differential inclusions with state-dependent delay
In this paper, we establish sufficient conditions for the existence of mild solutions for fractional integro-differential inclusions with state-dependent delay. The techniques rely on fractional calculus, multivalued mapping on a bounded set and Bohnenblust-Karlin's fixed point theorem. Finally, we present an example to illustrate the theory.
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 power function spaces associated to regular Sturm--Liouville problems.
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.
Fredholm alternatives and surjectivity results for multivalued -proper and condensing mappings with applications to nonlinear integral and differential equations
Fredholm determinants and the Evans function for difference equations
We develop a difference equations analogue of recent results by F. Gesztesy, K. A. Makarov, and the second author relating the Evans function and Fredholm determinants of operators with semi-separable kernels.