Volterra subdiffusion problems with weakly singular kernel describe the dynamics of processes well. The graded L1 scheme is often chosen to discretize such since it can handle singularity solution near $$t = 0$$ . In this paper, we propose a modification. We first split time interval [0, T] into $$[0, T_0]$$ and $$[T_0, T]$$ , where $$T_0$$ ( $$0< T_0 < T$$ ) reasonably small. Then, applied in ...

The theory of finitary biframes as order-theoretical duals bitopological spaces is explored. category a coreflective subcategory that biframes. Some the advantages adopting pointfree notion bispaces are studied. In particular, it shown for every biframe there which plays role analogue to assembly in frames: L A(L) with universal property analogous frame; and such its main component isomorphic o...

In this paper, we first define soft u-open sets and s-open as two new classes of on bitopological spaces. We show that the class p-open lies strictly between these classes, give several sufficient conditions for equivalence each sets, respectively. addition to these, introduce u-?-open, p-?-open, s-?-open three in spaces, which contain Via notions Lindelöfeness SBTSs. discuss relationship notio...