Monotone iterative technique for time-space fractional diffusion equations involving delay

Abstract

This paper considers the initial boundary value problem for the time-space fractional delayed diffusion equation with fractional Laplacian. By using the semigroup theory of operators and the monotone iterative technique, the existence and uniqueness of mild solutions for the abstract time-space evolution equation with delay under some quasimonotone conditions are obtained. Finally, the abstract results are applied to the time-space fractional delayed diffusion equation with fractional Laplacian operator, which improve and generalize the recent results of this issue.

An L1 type difference/Galerkin spectral scheme for variable-order time-fractional nonlinear diffusion–reaction equations with fixed delay

“…The wellposedness and the regularity of the solutions to Riemann-Liouville variable-order fractional nonlinear differential equations were discussed in [50,51]. As a special class of the problem under consideration, an initial boundary value problem for the fractional delayed semilinear diffusion equation with the fractional Laplacian was discussed in [52].…”

“…To the best of our knowledge, we can construct a maximum principle for the problem under consideration by invoking the methodology in [53] and by noticing the existence of a delay in (1.1)- (1.2). This can also be done by invoking the techniques of Barrier analysis in [52]. In the meantime, we investigate the problem's numerical solution and its convergence and stability analysis.…”

Upper and Lower Solution Method for a Singular Tempered Fractional Equation with a p-Laplacian Operator

“…Due to the widespread application of differential equations in practice, in recent decades, many theories and methods of nonlinear analysis, such as the spaces theories [26][27][28][29][30][31], smoothness theories [32][33][34][35], operator theories [36][37][38], fixed-point theorems [18,21,24,25,[39][40][41], subsuper solution methods [17,[42][43][44][45], monotone iterative techniques [12,[46][47][48][49][50][51][52][53] and the variational method [54][55][56][57][58], have been developed to study various differential equations. For example, by adopting the fixed point theorem of the mixed monotone operator, Zhou et.…”

Existence and global asymptotic behavior of S-asymptotically periodic solutions for fractional evolution equation with delay

“…On the other hand, the theory of delayed partial differential equations has a wide range of physical background and practical mathematical models. In the last decade, fractional evolution equations with delay have also been investigated extensively, and some interesting results have been obtained (see [6,11,18,20]).…”