scholarly journals Semilinear Cauchy Problems with Almost Sectorial Operators

2007 ◽  
Vol 55 (4) ◽  
pp. 333-346 ◽  
Author(s):  
Tomasz Dlotko
Keyword(s):  
Cauchy Problems ◽  
Sectorial Operators ◽  
Almost Sectorial Operators

Attractivity for fractional evolution equations with almost sectorial operators

2018 ◽  
Vol 21 (3) ◽  
pp. 786-800 ◽  
Author(s):  
Yong Zhou
Keyword(s):  
Evolution Equations ◽  
Sufficient Conditions ◽  
Cauchy Problems ◽  
Fractional Evolution Equations ◽  
Integer Order ◽  
Sectorial Operators ◽  
Almost Sectorial Operators ◽  
Globally Attractive

Abstract In this paper, we initiate the question of the attractivity of solutions for fractional evolution equations with almost sectorial operators. We establish sufficient conditions for the existence of globally attractive solutions for the Cauchy problems in cases that semigroup is compact as well as noncompact. Our results essentially reveal certain characteristics of solutions for fractional evolution equations, which are not possessed by integer order evolution equations.

scholarly journals Abstract fractional Cauchy problems with almost sectorial operators

2012 ◽  
Vol 252 (1) ◽  
pp. 202-235 ◽  
Author(s):  
Rong-Nian Wang ◽  
De-Han Chen ◽  
Ti-Jun Xiao
Keyword(s):  
Cauchy Problems ◽  
Sectorial Operators ◽  
Almost Sectorial Operators

scholarly journals Asymptotically almost periodic solutions of fractional relaxation inclusions with Caputo derivatives

2018 ◽  
Vol 104 (118) ◽  
pp. 23-41 ◽  
Author(s):  
Marko Kostic
Keyword(s):  
Fixed Point ◽  
Periodic Solutions ◽  
Fixed Point Theorems ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Periodic Coefficients ◽  
Sectorial Operators ◽  
Almost Sectorial Operators ◽  
Fractional Relaxation ◽  
Asymptotically Almost Periodic

We analyze asymptotically almost periodic solutions for a class of (semilinear) fractional relaxation inclusions with Stepanov almost periodic coefficients. As auxiliary tools, we use subordination principles, fixed point theorems and the well known results on the generation of infinitely differentiable degenerate semigroups with removable singularities at zero. Our results are well illustrated and seem to be not considered elsewhere even for fractional relaxation equations with almost sectorial operators.

scholarly journals Analysis of Hilfer Fractional Integro-Differential Equations with Almost Sectorial Operators

2021 ◽  
Vol 5 (1) ◽  
pp. 22
Author(s):  
Kulandhaivel Karthikeyan ◽  
Amar Debbouche ◽  
Delfim F. M. Torres
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Derivatives ◽  
Sectorial Operators ◽  
Fundamental Properties ◽  
Almost Sectorial Operators ◽  
Fixed Point Technique

In this work, we investigate a class of nonlocal integro-differential equations involving Hilfer fractional derivatives and almost sectorial operators. We prove our results by applying Schauder’s fixed point technique. Moreover, we show the fundamental properties of the representation of the solution by discussing two cases related to the associated semigroup. For that, we consider compactness and noncompactness properties, respectively. Furthermore, an example is given to illustrate the obtained theory.

scholarly journals Mild Solutions for Impulsive Integro-Differential Equations Involving Hilfer Fractional Derivative with almost Sectorial Operators

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 313
Author(s):  
Kulandhaivel Karthikeyan ◽  
Panjaiyan Karthikeyan ◽  
Nichaphat Patanarapeelert ◽  
Thanin Sitthiwirattham
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Jump Conditions ◽  
Hilfer Fractional Derivative ◽  
Sectorial Operators ◽  
Almost Sectorial Operators ◽  
Suitable Definition ◽  
Definition Of

In this manuscript, we establish the mild solutions for Hilfer fractional derivative integro-differential equations involving jump conditions and almost sectorial operator. For this purpose, we identify the suitable definition of a mild solution for this evolution equations and obtain the existence results. In addition, an application is also considered.

Sign in / Sign up

Export Citation Format

Share Document