Mean-value theorems and the nonoscillatory nature of solutions of partial differential equations in the spaces En and Pn

1992 ◽  
Vol 44 (11) ◽  
pp. 1359-1365 ◽  
Author(s):  
M. K. Bugir
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Mean Value ◽  
Partial Differential ◽  
Mean Value Theorems

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.

scholarly journals APPLICATION OF FUNCTIONAL RELATIONS TO MODELING BY MEANS OF DIFFERENTIAL EQUATIONS

2020 ◽  
pp. 454-458
Author(s):  
E. Kenenbaev ◽  
Dzh. A. Akerova ◽  
L. Askar kyzy
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Hermite Interpolation ◽  
Interpolation Polynomial ◽  
Mean Value ◽  
Elliptic Type ◽  
Partial Differential ◽  
Functional Relations ◽  
Finite Set ◽  
Hermite Interpolation Polynomial

Modeling by means of differential equations is considered in the paper. Their solutions are constructed on the base of functional relations connecting values of a solution of the equation in different points (infinite or finite set of values). For examples, even, odd and periodical solutions, Vallée-Poussin’s assertion, Lagrange interpolation polynomial, Hermite interpolation polynomial, spline-functions for ordinary differential equations, Asgeirsson’s identity and its generalizations for partial differential equations of hyperbolic type, “mean value” for partial differential equations of elliptic type are considered. Also, if an equation is close to one of considered types then an assertion is to be fulfilled approximately. Some estimations are found for such examples. An application of such relations to investigate some problems of interpolation and extrapolation is demonstrated.

scholarly journals Nonlinear discrete fractional sum inequalities related to the theory of discrete fractional calculus with applications

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zareen A. Khan ◽  
Fahd Jarad ◽  
Aziz Khan ◽  
Hasib Khan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Calculus ◽  
Mean Value ◽  
Discrete Fractional Calculus ◽  
Partial Differential ◽  
Examination Procedure ◽  
The Mean ◽  
New Form

AbstractBy means of ς fractional sum operator, certain discrete fractional nonlinear inequalities are replicated in this text. Considering the methodology of discrete fractional calculus, we establish estimations of Gronwall type inequalities for unknown functions. These inequalities are of a new form comparative with the current writing discoveries up until this point and can be viewed as a supportive strategy to assess the solutions of discrete partial differential equations numerically. We show a couple of employments of the compensated inequalities to reflect the benefits of our work. The main outcomes might be demonstrated by the use of the examination procedure and the approach of the mean value hypothesis.

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