In this article,we study the approximate controllability of neutral partial differential equations with Hilfer fractional derivative and not instantaneous impulses effects.By using the Sadovskii's fixed point theo...In this article,we study the approximate controllability of neutral partial differential equations with Hilfer fractional derivative and not instantaneous impulses effects.By using the Sadovskii's fixed point theorem,fractional calculus and resolvent operator functions,we prove the approximate controllability of the considered system.展开更多
The authors compared isoenzymes of five enzymes and soluble protein in Arthrospira platensis (A3) and A. erdosensis (A4) from alkaline lakes in Erdos Plateau, Nei Monggo (Inner Mongalia), China and exotic species of A...The authors compared isoenzymes of five enzymes and soluble protein in Arthrospira platensis (A3) and A. erdosensis (A4) from alkaline lakes in Erdos Plateau, Nei Monggo (Inner Mongalia), China and exotic species of A. platensis (A1) from Chad and A. maxima (A2) from Mexico by means of polyacrylamide gel electrophoresis. The results showed that the isoenzymes of EST, POD and soluble protein were polymorphic. Monomorphism and polymorphism were found in isoenzymes of AMY, CAT and SOD, and monomorphism was found only in the introduced species. The isoenzymes and soluble protein of the local species are all polymorphic. The number of bands in these species were in the order of A3>A4>A1>A2. A2 is the most primary, A1 from Chad Lake is relatively primary, A3 and A4 are ad- vanced species in evolution. Cluster analysis showed that the relation between the two introduced species are the closest to each other, and so too are the two local ones.展开更多
The aim of this paper is to study the exact controllability of the Petrovsky equation. Under some checkable geometric assumptions, we establish the observability inequality via the multiplier method for the Dirichlet ...The aim of this paper is to study the exact controllability of the Petrovsky equation. Under some checkable geometric assumptions, we establish the observability inequality via the multiplier method for the Dirichlet control problem.展开更多
In this paper,we consider the existence and uniqueness of the mild solutions for a class of fractional non-autonomous evolution equations with delay and Caputo's fractional derivatives.By using the measure of nonc...In this paper,we consider the existence and uniqueness of the mild solutions for a class of fractional non-autonomous evolution equations with delay and Caputo's fractional derivatives.By using the measure of noncompactness,β-resolvent family,fixed point theorems and Banach contraction mapping principle,we improve and generalizes some related results on this topic.At last,we give an example to illustrate the application of the main results of this paper.展开更多
基金Supported by Shandong University of Finance and Economics 2023 International Collaborative Projectsthe National Natural Science Foundation of China(Grant No.62073190)。
文摘In this article,we study the approximate controllability of neutral partial differential equations with Hilfer fractional derivative and not instantaneous impulses effects.By using the Sadovskii's fixed point theorem,fractional calculus and resolvent operator functions,we prove the approximate controllability of the considered system.
基金This work was supported by NSFC (No. 30460104), NFS project of Nei Monggo (No. 200308020310) and the Scientific Research Founda-tion for Universities of Nei Monggo (No. NJ04036)
文摘The authors compared isoenzymes of five enzymes and soluble protein in Arthrospira platensis (A3) and A. erdosensis (A4) from alkaline lakes in Erdos Plateau, Nei Monggo (Inner Mongalia), China and exotic species of A. platensis (A1) from Chad and A. maxima (A2) from Mexico by means of polyacrylamide gel electrophoresis. The results showed that the isoenzymes of EST, POD and soluble protein were polymorphic. Monomorphism and polymorphism were found in isoenzymes of AMY, CAT and SOD, and monomorphism was found only in the introduced species. The isoenzymes and soluble protein of the local species are all polymorphic. The number of bands in these species were in the order of A3>A4>A1>A2. A2 is the most primary, A1 from Chad Lake is relatively primary, A3 and A4 are ad- vanced species in evolution. Cluster analysis showed that the relation between the two introduced species are the closest to each other, and so too are the two local ones.
基金Supported by the Natural Science Foundation of Hainan Province(No.20161011)
文摘The aim of this paper is to study the exact controllability of the Petrovsky equation. Under some checkable geometric assumptions, we establish the observability inequality via the multiplier method for the Dirichlet control problem.
基金The paper is supported financially by the Project of Shandong Province Higher Educational Science and Technology Program(J16LI14)the National Natural Science Foundation of China(No.11871302)+2 种基金the Taishan Scholars Program of Shandong Province(No.tsqn20161041)the Humanities and Social Sciences Project of the Ministry Education of China(No.19YJA910002)the Natural Science Foundation of Shandong Province(No.ZR2018MG002).
文摘In this paper,we consider the existence and uniqueness of the mild solutions for a class of fractional non-autonomous evolution equations with delay and Caputo's fractional derivatives.By using the measure of noncompactness,β-resolvent family,fixed point theorems and Banach contraction mapping principle,we improve and generalizes some related results on this topic.At last,we give an example to illustrate the application of the main results of this paper.
