On continuity of the fractional derivative of the time-fractional semilinear pseudo-parabolic systems

• Published in: Advances in difference equations Vol. 2021; no. 1; pp. 1 - 24
• Main Authors: Karapinar, Erdal, Binh, Ho Duy, Luc, Nguyen Hoang, Can, Nguyen Huu
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 23-01-2021; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Boundary value problems; Caputo derivative; Continuity; Difference and Functional Equations; Functional Analysis; Initial value problem; Mathematics; Mathematics and Statistics; Nonlinear equations; Nonlinear fractional pseudo-parabolic equation systems; Ordinary Differential Equations; Partial Differential Equations; Regularity; Nonlinear fractional pseudo-parabolic equation systems; 35K70; 35K92; Initial value problem; Caputo derivative; 47J06; Regularity; 47A52; 35K55
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-021-03232-z

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.