The paper discusses the asymptotic properties of solutions of the scalar functional differential equation . Asymptotic formulas are given in terms of solutions of the appropriate scalar functional nondifferential equation.
The paper discusses the asymptotic properties of solutions of the scalar functional differential equation of the advanced type. We show that, given a specific asymptotic behaviour, there is a (unique) solution which behaves in this way.
We discuss the asymptotic behaviour of all solutions of the functional differential equation where . The asymptotic bounds are given in terms of a solution of the functional nondifferential equation
The paper contains applications of Schrőder’s equation to differential equations with a deviating argument. There are derived conditions under which a considered equation with a deviating argument intersecting the identity can be transformed into an equation with a deviation of the form . Moreover, if the investigated equation is linear and homogeneous, we introduce a special form for such an equation. This special form may serve as a canonical form suitable for the investigation of oscillatory...
We investigate simultaneous solutions of a system of Schroder's functional equations. Under certain assumptions these solutions are used in transformations of functional-differential equations the initial set of which consists of the initial point only.
In this paper we investigate the asymptotic properties of all solutions of the delay differential equation y’(x)=a(x)y((x))+b(x)y(x), xI=[x0,). We set up conditions under which every solution of this equation can be represented in terms of a solution of the differential equation z’(x)=b(x)z(x), xI and a solution of the functional equation |a(x)|((x))=|b(x)|(x), xI.
The paper discusses basics of calculus of backward fractional differences and sums. We state their definitions, basic properties and consider a special two-term linear fractional difference equation. We construct a family of functions to obtain its solution.
Článek přináší základní pohled na oblast tzv. zlomkového kalkulu, tedy partii matematické analýzy, která je věnována derivacím neceločíselných řádů a souvisejícím otázkám. Je zde popsán historický vývoj tohoto pojmu, včetně motivací a aplikací. Speciálně se pak text zaměřuje na oblast diferenciálních rovnic s neceločíselnými derivacemi, na základní otázky spojené s jejich vyšetřováním a také na některé nové výzvy, které tato disciplína přináší.
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