In this paper, we consider the numerical inverse Laplace transform for distributed order time-fractional equations, where a discontinuous Galerkin scheme is used to discretize problem in space. The success of Talbot’s approach computation depends critically on problem’s spectral properties and present method numerically enclose spectrum compute resolvent estimates independent size. new results ...

where D is the Caputo fractional derivative of order α with  < α < , A :D(A)⊂ X → X is the infinitesimal generator of a resolvent Sα(t), t ≥ , B : U → X is a bounded linear operator, u ∈ L([,b],U), X and U are two real Hilbert spaces, J–α t h denotes the  – α order fractional integral of h ∈ L([,b],X). The controllability problem has attracted a lot of mathematicians and engineers’ att...

Equations from heat conduction and viscoelasticity are written as x′(t) = A [ x(t) + ∫ t 0 F (t− s)x(s)ds ] + f(t), t ≥ 0, x(0) = x0, (1) in a Banach space X, where A is a closed and densely defined operator and F (t) is a bounded operator for t ≥ 0. We obtain the equivalence between the resolvent operator of Eq.(1) and solutions of d dt 〈x(t), v〉 = 〈x(t) + ∫ t 0 F (t− s)x(s)ds,A∗v〉+ 〈f(t), v〉,...

Recent development in ruin theory has seen growing popularity of jump diffusion processes in modeling an insurer’s assets and liabilities. Despite the variations of technique, the analysis of ruin-related quantities mostly relies on solutions to certain differential equations. In this paper, we propose in the context of Lévy-type jump diffusion risk models a solution method to a general class o...

This paper is devoted to a class of impulsive fractional semilinear integrodifferential equations with nonlocal initial conditions. Based on the semigroup theory and some fixed point theorems, existence PC-mild solutions established under condition compact resolvent operator. Furthermore, uniqueness proved in case noncompact

The purpose of this paper is to introduce and study a new kind of generalized strongly nonlinear operator inclusion problems involving generalized m-accretive mapping in Banach spaces. By using the resolvent operator technique for generalized m-accretive mapping due to Huang and Fang, we also prove the existence theorem of the solution for this kind of operator inclusion problems and construct ...

We demonstrate a pair of new product formulæ which combine a projection with a resolvent of a positive operator, or with an exponential function and spectral projections, respectively. The convergence is strong or even operator-norm under more restrictive assumptions. The second mentioned formula can be used to describe Zeno dynamics in the situation when the usual non-decay measurement is repl...

A new system of nonlinear variational inclusions involving A, η -monotone mappings in the framework of Hilbert space is introduced and then based on the generalized resolvent operator technique associated with A, η -monotonicity, the approximation solvability of solutions using an iterative algorithm is investigated. Since A, η -monotonicity generalizes A-monotonicity and Hmonotonicity, our res...