Maximum Principles for Multi-Term Space-Time Variable-Order Fractional Diffusion Equations and their Applications

Abstract In this paper, we deal with maximum principles for multi-term space-time variable-order Riesz-Caputo fractional differential equations (MT-STVO-RCFDEs, for short). We firstly derive several important inequalities for variable-order fractional derivatives at extreme points. Based on these inequalities, we obtain the maximum principles. Finally, these principles are employed to show that the uniqueness of solutions of the (MT-STVO-RCFDEs) and continuous dependance of solutions on initial-boundary value conditions.

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