Smoothing effect and regularity for evolution integrodifferential systems
Smoothness in fractional evolution equations and conservation laws
Smoothness Properties of Solutions of Caputo-Type Fractional Differential Equations
Mathematics Subject Classification: 26A33, 34A25, 45D05, 45E10We consider ordinary fractional differential equations with Caputo-type differential operators with smooth right-hand sides. In various places in the literature one can find the statement that such equations cannot have smooth solutions. We prove that this is wrong, and we give a full characterization of the situations where smooth solutions exist. The results can be extended to a class of weakly singular Volterra integral equations.
Solution forte pour des équations intégro-différentielles non linéaires paraboliques
Solution of a class of the first kind singular integral equation with multiplicative Cauchy kernel
In the present paper, we give the exact solutions of a singular equation with logarithmic singularities in two classes of functions and construct formulae for the approximate solutions.
Solution of a linear integral equation of third kind.
Solution of an integral equation with a logarithmic kernel.
Solution of Cauchy-type singular integral equations of the first kind with zeros of Jacobi polynomials as interpolation nodes.
Solution of Fredholm integrodifferential equation for an infinite elastic plate
Many authors discussed the problem of an elastic infinite plate with a curvilinear hole, some of them considered this problem in z-plane and the others in the s-plane. They obtained an exact expression for Goursat's functions for the first and second fundamental problem. In this paper, we use the Cauchy integral method to obtain a solution to the first and second fundamental problem by using a new transformation. Some applications are investigated and also some special cases are discussed.
Solution of nonlinear Fredholm-Hammerstein integral equations by using semiorthogonal spline wavelets.
Solution of nonlinear Volterra-Hammerstein integral equations via single-term Walsh series method.
Solution of nonlinear Volterra-Hammerstein integral equations via rationalized Haar functions.
Solution of some parabolic integro-differential equations by means of the algebraic operational calculus of distributions.
Solution of Volterra-type integro-differential equations with a generalized Lauricella confluent hypergeometric function in the kernels.
Solution semigroup and invariant manifolds for functional equations with infinite delay
It is proved that parabolic equations with infinite delay generate -semigroup on the space of initial conditions, such that local stable and unstable manifolds can be constructed for a fully nonlinear problems with help of usual methods of the theory of parabolic equations.
Solution stationnaire de l'équation de coagulation de gouttelettes en chute avec le vent horizontal
Solution to Fredholm integral inclusions via ( F, δ b )-contractions
We present sufficient conditions for the existence of solutions of Fredholm integral inclusion equations using new sort of contractions, named as multivalued almost F -contractions and multivalued almost F -contraction pairs under ı-distance, defined in b-metric spaces. We give its relevance to fixed point results in orbitally complete b-metric spaces. To rationalize the notions and outcome, we illustrate the appropriate examples.
Solutions for a class of integro-differential equations with time periodic coefficients.
Solutions for singular Volterra integral equations.
Solutions of singular integral equations.