Some Properties of Impedance as a Causal Operator

1962 ◽  
Vol 3 (2) ◽  
pp. 262-271 ◽  
Author(s):  
Tai Tsun Wu
Keyword(s):  
Causal Operator

scholarly journals THE EXISTENCE OF THE EXTREMAL SOLUTION FOR THE BOUNDARY VALUE PROBLEMS OF VARIABLE FRACTIONAL ORDER DIFFERENTIAL EQUATION WITH CAUSAL OPERATOR

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040025
Author(s):  
JINGFEI JIANG ◽  
JUAN L. G. GUIRAO ◽  
TAREQ SAEED
Keyword(s):  
Differential Equation ◽  
Fractional Order ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Existence Results ◽  
Extremal Solution ◽  
Variable Order ◽  
Fractional Order Differential Equation ◽  
Causal Operator ◽  
Linear Differential

In this study, the two-point boundary value problem is considered for the variable fractional order differential equation with causal operator. Under the definition of the Caputo-type variable fractional order operators, the necessary inequality and the existence results of the solution are obtained for the variable order fractional linear differential equations according to Arzela–Ascoli theorem. Then, based on the proposed existence results and the monotone iterative technique, the existence of the extremal solution is studied, and the relative results are obtained based on the lower and upper solution. Finally, an example is provided to illustrate the validity of the theoretical results.

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