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Displaying similar documents to “Stability of a monotonic solution of a non-autonomous multidimensional delay differential equation of arbitrary (fractional) order.”

Fractional BVPs with strong time singularities and the limit properties of their solutions

Svatoslav Staněk (2014)

Open Mathematics

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In the first part, we investigate the singular BVP d d t c D α u + ( a / t ) c D α u = ℋ u , u(0) = A, u(1) = B, c D α u(t)|t=0 = 0, where ℋ 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 d d t c D α n u + ( a / t ) c D α n u = f ( t , u , c D β n u ) , u(0) = A, u(1) = B, c D α n u ( t ) t = 0 = 0 where a < 0, 0 < β n ≤ α n < 1, limn→∞ β n = 1, and solutions of u″+(a/t)u′ = f(t,...

Functional-differential equations with Riemann-Liouville integrals in the nonlinearities

Milan Medveď (2014)

Mathematica Bohemica

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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...