In this paper, we establish a sufficient conditions for the nonlocal controllability of mixed VolterraFredholm type fractional semilinear integro-differential inclusions in Banach spaces. The results are obtained by using fractional calculus, operator semigroups and Bohnenblust-Karlin’s fixed point theorem. Finally, an example is given to illustrate the theoretical results.

This paper is concerned with semilinear differential equations with nonlocal conditions in Banach spaces. Using the tools involving the measure of noncompactness and fixed point theory, existence of mild solutions is obtained without the assumption of compactness or equicontinuity on the associated linear semigroup.

In these lectures we shall present an introduction of the theory of stochastic integration in UMD Banach spaces and some of its applications. The Hilbert space approach to stochastic partial differential equations (SPDEs) was pioneered in the 1980s by Da Prato and Zabczyk. Under suitable Lipschitz conditions, mild solutions of semilinear SPDEs in Hilbert spaces can be obtained by solving a fixe...

We construct global-in-time solutions for semilinear parabolic rough partial differential equations. work on a scale of Banach spaces tailored to the controlled path approach and derive suitable priori estimates solution which do not contain quadratic terms.

The object of the investigation is to study reducible $M$-ideals in Banach spaces. It is shown that if the number of $M$-ideals in a Banach space $X$ is $n(<infty)$, then the number of reducible $M$-ideals does not exceed of $frac{(n-2)(n-3)}{2}$. Moreover, given a compact metric space $X$, we obtain a general form of a reducible $M$-ideal in the space $C(X)$ of continuous functions on $X$. The...

In this article we develop convergence theory for a general class of adaptive approximation algorithms for abstract nonlinear operator equations on Banach spaces, and then use the theory to obtain convergence results for practical adaptive finite element methods (AFEM) applied to several classes of nonlinear elliptic equations. In the first part of the paper, we develop a weak-* convergence fra...

In this article, we discuss an age-structured SIR model in which disease spread not only through direct person-to-person contacts, but also indirect contacts. It is evident that age plays a crucial role SARS virus infection including COVID-19 infection. We formulate our as abstract semilinear Cauchy problem appropriate Banach space to show the existence of solution and steady states. study, it ...

We study a Cauchy problem of class nonconvex second-order integro-differential inclusions and boundary value associated to semilinear evolution inclusion defined by nonlocal conditions in non-separable Banach spaces. The existence mild solutions is established under Filippov type assumptions.