Advances in Difference Equations (Jan 2021)
On continuity of the fractional derivative of the time-fractional semilinear pseudo-parabolic systems
Abstract
Abstract In this work, we study an initial value problem for a system of nonlinear parabolic pseudo equations with Caputo fractional derivative. Here, we discuss the continuity which is related to a fractional order derivative. To overcome some of the difficulties of this problem, we need to evaluate the relevant quantities of the Mittag-Leffler function by constants independent of the derivative order. Moreover, we present an example to illustrate the theory.
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