Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Abstract non-scalar Volterra difference equations

Marko Kostić

Abstract

In this paper, we investigate the abstract non-scalar Volterra difference equations. We employ the Poisson like transforms to connect the solutions of the abstract non-scalar Volterra integro-differential equations and the abstract non-scalar Volterra difference equations. We also investigate the existence, uniqueness and almost periodicity of solutions to the abstract multi-term fractional difference equations with Weyl fractional derivatives.

Abstract non-scalar Volterra difference equations

Abstract

In this paper, we investigate the abstract non-scalar Volterra difference equations. We employ the Poisson like transforms to connect the solutions of the abstract non-scalar Volterra integro-differential equations and the abstract non-scalar Volterra difference equations. We also investigate the existence, uniqueness and almost periodicity of solutions to the abstract multi-term fractional difference equations with Weyl fractional derivatives.
Paper Structure (7 sections, 11 theorems, 83 equations)

This paper contains 7 sections, 11 theorems, 83 equations.

Table of Contents

  1. Introduction and preliminaries
  2. Abstract non-scalar Volterra integral equations
  3. Discrete $(A,k,B)$-regularized $C$-resolvent families
  4. $(k,C,B,(A_{i})_{1\leq i\leq n},(v_{i})_{1\leq i\leq n})$-solution operator families
  5. The well-posedness and asymptotically almost periodic type solutions of the corresponding discrete abstract Cauchy problems
  6. The abstract multi-term fractional difference equations with Weyl fractional derivatives
  7. Conclusions and final remarks

Key Result

Proposition 2.2

Suppose that a sequence $(u_{k})_{k\in {\mathbb N}_{0}}$ is a solution of 123123 and the operator $B(v)-A(0)$ is injective for all $v\in {\mathbb N}_{0}.$ Then $u(\cdot)$ is uniquely determined.

Theorems & Definitions (31)

  • Definition 1.1
  • Definition 1.2
  • Definition 1.3
  • Definition 2.1
  • Proposition 2.2
  • proof
  • Proposition 2.3
  • proof
  • Theorem 2.4
  • proof
  • ...and 21 more