partial differential inclusions
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2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Qiaomin Xiang ◽  
Pengxian Zhu

The topological structure of solution sets for the Sobolev-type fractional order delay systems with noncompact semigroup is studied. Based on a fixed point principle for multivalued maps, the existence result is obtained under certain mild conditions. With the help of multivalued analysis tools, the compactness of the solution set is also obtained. Finally, we apply the obtained abstract results to the partial differential inclusions.



Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Nayyar Mehmood ◽  
Ahmed Al-Rawashdeh ◽  
Akbar Azam

In this article we prove the existence results for solutions of the Darboux-type problems in fuzzy partial differential inclusions with local conditions of integral types. We present two problems involving open and closed level sets of a given fuzzy mapping. In the first case fuzzy differential inclusion has been transformed into an equivalent Darboux-type problem for partial differential equations and then using the Tychonoff fixed point theorem we prove the existence result for this crisp case. For the second case we use Nadler’s fixed point theorem and selection theorem of Kuratowski-Ryll-Nardzewski to find the solution of given differential inclusions problem. We furnish an example to validate our results.



2018 ◽  
Vol 35 (2) ◽  
pp. 2547-2557
Author(s):  
Maliha Rashid ◽  
Nayyar Mehmood ◽  
Sumbal Shaheen


2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Nayyar Mehmood ◽  
Akbar Azam

We discuss the existence of solution of a certain type of fuzzy partial differential inclusions with local conditions of integral types.



2013 ◽  
Vol 13 (1) ◽  
pp. 95-118 ◽  
Author(s):  
Janosch Rieger

Abstract. This paper presents the first feasible method for the approximation of solution sets of semi-linear elliptic partial differential inclusions. It is based on a new Galerkin Finite Element approach that projects the original differential inclusion to a finite-dimensional subspace of . The problem that remains is to discretize the unknown solution set of the resulting finite-dimensional algebraic inclusion in such a way that efficient algorithms for its computation can be designed and error estimates can be proved. One such discretization and the corresponding basic algorithm are presented along with several enhancements, and the algorithm is applied to two model problems.



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