Problems with different time scales for partial differential equations

1980 ◽  
Vol 33 (3) ◽  
pp. 399-439 ◽  
Author(s):  
Heinz-Otto Kreiss
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Time Scales ◽  
Partial Differential ◽  
Different Time Scales

scholarly journals Discrete Fractional Inequalities Pertaining a Fractional Sum Operator with Some Applications on Time Scales

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Zareen A. Khan ◽  
Kamal Shah
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Calculus ◽  
Time Scales ◽  
Mean Value ◽  
Assessment Procedure ◽  
Discrete Fractional Calculus ◽  
Partial Differential ◽  
Unique Structure

This content replicates some discrete nonlinear fractional inequalities by virtue of the fractional sum operator Ψ ¯ on time scales. Through the recognition of the principle of discrete fractional calculus, we are able to recover the precise estimates for unknown functions of inequalities of the Gronwall type. The resultant inequalities are of unique structure comparative with the latest reviewing disclosures and can be described as a complementary tool for numerically testing the solutions of discrete partial differential equations. The foremost consequences are probably confirmed via handling of assessment procedure and technique of mean value speculation. We display few examples of the proposed inequalities to represent the incentives of our effort.

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