Almost sectorial operators on Ψ‐Hilfer derivative fractional impulsive integro‐differential equations

2021 ◽  
Author(s):  
Kulandhivel Karthikeyan ◽  
Panjaiyan Karthikeyan ◽  
Haci Mehmet Baskonus ◽  
Kuppusamy Venkatachalam ◽  
Yu‐Ming Chu
Keyword(s):  
Differential Equations ◽  
Sectorial Operators ◽  
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.

scholarly journals Analysis on ψ-Hilfer Fractional Impulsive Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1895
Author(s):  
Kulandhaivel Karthikeyan ◽  
Panjaiyan Karthikeyan ◽  
Dimplekumar N. Chalishajar ◽  
Duraisamy Senthil Raja ◽  
Ponnusamy Sundararajan
Keyword(s):  
Differential Equations ◽  
Impulsive Differential Equations ◽  
Strong Relationship ◽  
Dimensional System ◽  
Structural Investigations ◽  
Sectorial Operators ◽  
Higher Dimensional ◽  
Almost Sectorial Operators ◽  
Special Cases

In this manuscript, we establish the existence of results of fractional impulsive differential equations involving ψ-Hilfer fractional derivative and almost sectorial operators using Schauder fixed-point theorem. We discuss two cases, if the associated semigroup is compact and noncompact, respectively. We consider here the higher-dimensional system of integral equations. We present herewith new theoretical results, structural investigations, and new models and approaches. Some special cases of the results are discussed as well. Due to the nature of measurement of noncompactness theory, there exists a strong relationship between the sectorial operator and symmetry. When working on either of the concepts, it can be applied to the other one as well. Finally, a case study is presented to demonstrate the major theory.

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.

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