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Controllability for some partial functional integrodifferential equations with nonlocal conditions in Banach spaces

100%

Ezzinbi K. , Degla G. , Ndambomve P.

tom 35

nr 1

25-46

This work concerns the study of the controllability of some partial functional integrodifferential equation with nonlocal initial conditions in Banach spaces. It gives sufficient conditions that ensure the controllability of the system by supposing that its linear homogeneous part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point theorem. As a result, we obtain a generalization of the work of Y.K. Chang, J.J. Nieto and W.S. Li (J. Optim. Theory Appl. 142, 267-273 (2009)), without assuming the compactness of the resolvent operator. An example of application is given for illustration.

On the hybrid Caputo-proportional fractional differential inclusions in Banach spaces

86%

Abbas M. I.

Journal of Mathematics and Applications

2022

tom Vol. 45

5--20

The current article concerns an existence criteria of solutions of nonlinear fractional differential inclusions in the sense of the hybrid Caputo-proportional fractional derivatives in Banach space. The investigation of the main result relies on the set-valued issue of Mönch fixed point theorem incorporated with the Kuratowski measure of non-compactness.

Approximate controllability results in α-norm for some partial functional integrodifferential equations with nonlocal initial conditions in Banach spaces

86%

Ndambomve P. , Kpoumie M. E.-K. , Ezzinbi K.

Journal of Applied Analysis

2023

tom Vol. 29, nr 1

127--142

In this work, we discuss the approximate controllability of some nonlinear partial functional integrodifferential equations with nonlocal initial condition in Hilbert spaces.We assume that the corresponding linear part is approximately controllable. The results are obtained by using fractional power theory and α-norm, the measure of noncompactness and theMönch fixed-point theorem, and the theory of analytic resolvent operators for integral equations. As a result, we obtain a generalization of the work of Mahmudov [N. I. Mahmudov, Approximate controllability of evolution systems with nonlocal conditions, Nonlinear Anal. 68 (2008), no. 3, 536-546], without assuming the compactness of the resolvent operator. Our results extend and complement many other important results in the literature. Finally, a concrete example is given to illustrate the application of the main results.

Controllability of multi-term time-fractional differential systems with state-dependent delay

72%

Chaudhary R. , Singh V. , Pandey D. N.

2020

tom Vol. 26, nr 2

241--255

In this paper, controllability results for a class of multi-term time-fractional differential systems with state-dependent delay have been studied. The concept of fractional calculus, measure of noncompactness and Mönch fixed-point theorem has been implemented to obtain a new set of controllability results. Finally, an application is given to illustrate the obtained results.