scholarly journals Exact Analytical Wave Solutions for Space-Time Variable-Order Fractional Modified Equal Width Equation

2022 ◽  
pp. 105216
Author(s):  
Umair Ali ◽  
Hijaz Ahmad ◽  
Jamel Baili ◽  
Thongchai Botmart ◽  
Maha A Aldahlan
Keyword(s):  
Space Time ◽  
Time Variable ◽  
Variable Order ◽  
Wave Solutions

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

2016 ◽  
Vol 19 (1) ◽  
Author(s):  
Zhenhai Liu ◽  
Shengda Zeng ◽  
Yunru Bai
Keyword(s):  
Extreme Points ◽  
Initial Boundary ◽  
Space Time ◽  
Time Variable ◽  
Maximum Principles ◽  
Variable Order ◽  
Uniqueness Of Solutions ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
Initial Boundary Value

AbstractIn 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.

scholarly journals On the sub–diffusion fractional initial value problem with time variable order

2021 ◽  
Vol 10 (1) ◽  
pp. 1301-1315
Author(s):  
Eduardo Cuesta ◽  
Mokhtar Kirane ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad
Keyword(s):  
Asymptotic Behavior ◽  
Fractional Derivative ◽  
Initial Value Problem ◽  
Regularity Result ◽  
Time Variable ◽  
Variable Order ◽  
Initial Value ◽  
Integration By Parts ◽  
Integration By Parts Formula ◽  
Variable Order Fractional Derivative

Abstract We consider a fractional derivative with order varying in time. Then, we derive for it a Leibniz' inequality and an integration by parts formula. We also study an initial value problem with our time variable order fractional derivative and present a regularity result for it, and a study on the asymptotic behavior.

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