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The study of the blow-up phenomenon for fractional reaction–diffusion problems is generally deemed of great importance in dealing with several situations that impact our daily lives, and it is applied in many areas such as finance and economics. In this article, we expand on some previous blow-up results for the explicit values and numerical simulation of finite-time blow-up solutions for a semilinear fractional partial differential problem involving a positive power of the solution. We show the behavior solution of the fractional problem, and the numerical solution of the finite-time blow-up solution is also considered. Finally, some illustrative examples and comparisons with the classical problem with integer order are presented, and the validity of the results is demonstrated. [ABSTRACT FROM AUTHOR]

In this paper, we evaluate certain type superlinear nonlocal problems that are a class of parabolic equations with the second-type integral condition. We use the Fadeo-Galarkin method to establish the existence of the weak solution and we prove the uniqueness of this solution for the problem by using an a priori estimate. In addition, we study the theoretical blow-up solution and perform several numerical simulations of finite-time blow-up of a particular example of the main problem. [ABSTRACT FROM AUTHOR]