scholarly journals Generalized Conformable Mean Value Theorems with Applications to Multivariable Calculus

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Francisco Martínez ◽  
Inmaculada Martínez ◽  
Mohammed K. A. Kaabar ◽  
Silvestre Paredes
Keyword(s):  
Research Work ◽  
Mean Value ◽  
Higher Order ◽  
Conformable Derivative ◽  
Mean Value Theorems ◽  
Classical Calculus ◽  
Multivariable Calculus ◽  
Conformable Derivatives ◽  
The Mean ◽  
Derivatives Of

The conformable derivative and its properties have been recently introduced. In this research work, we propose and prove some new results on the conformable calculus. By using the definitions and results on conformable derivatives of higher order, we generalize the theorems of the mean value which follow the same argument as in the classical calculus. The value of conformable Taylor remainder is obtained through the generalized conformable theorem of the mean value. Finally, we introduce the conformable version of two interesting results of classical multivariable calculus via the conformable formula of finite increments.

scholarly journals Modeling of pressure–volume controlled artificial respiration with local derivatives

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bahar Acay ◽  
Mustafa Inc ◽  
Yu-Ming Chu ◽  
Bandar Almohsen
Keyword(s):  
Efficient Solution ◽  
Clinical Medicine ◽  
Artificial Respiration ◽  
Pd Controller ◽  
Governing Equations ◽  
Conformable Derivative ◽  
Solution Methods ◽  
Conformable Derivatives ◽  
Derivatives Of ◽  
Volume Controlled

AbstractWe attempt to motivate utilization of some local derivatives of arbitrary orders in clinical medicine. For this purpose, we provide two efficient solution methods for various problems that occur in nature by employing the local proportional derivative defined by the proportional derivative (PD) controller. Under some necessary assumptions, a detailed exposition of the instantaneous volume in a lung is furnished by conformable derivative and such modified conformable derivatives as truncated M-derivative and proportional derivative. Moreover, we wish to investigate the performance of the above-mentioned operators in applications by plotting several graphs of the governing equations.

scholarly journals Effects of Ingested Fresh Palm Wine on Pupil Diameter and Amplitude of Accommodation in Young Adults

2021 ◽  
Vol 11 (9) ◽  
pp. 203-208
Author(s):  
Ugwoke, G.I. ◽  
Esenwah, E.C. ◽  
Ikoro, N.C.
Keyword(s):  
Young Adults ◽  
Pupil Diameter ◽  
Research Work ◽  
Mean Amplitude ◽  
Physicochemical Analysis ◽  
Mean Value ◽  
Normal Body Mass Index ◽  
Microbiological Analysis ◽  
Palm Wine ◽  
The Mean

Palm wine has long been the traditional wine of choice for most people during festive periods and social activities. This research work was done to determine the effect of ingested fresh palm wine on pupil diameter and amplitude of accommodation in young adults. Fifty (50) young adults aged between 18-35 years with a mean age of 23.46(±2.54) and weight ranging from 45-80kg with mean weight of 61.18(±8.00) volunteered for this work. The volunteers had normal body mass index (BMI) of between 18.5 and 25kg/m2. Pupil diameter in millimeters (mm) and Amplitude of Accommodation (AA) in diopters (D) were measured before and after 30 minutes, 60 minutes and 90 minutes intake of 330ml of fresh palm wine containing 5.1% alcohol at the time it was consumed. Physicochemical analysis of the palm wine showed the presence of Solids, Sugar, Ascorbic acid (Vitamin C) while microbiological analysis showed the presence of yeasts. Its pH at the time was 6.20. Statistical analysis with SPSS version 21 showed that the mean pupil diameter before intake of fresh palm wine was 3.80(±0.72) and mean value 30 minutes, 60 minutes and 90 minutes after intake of fresh palm wine were 3.30(±0.61), 3.48(±0.75) and 4.20(±0.64) respectively. The mean Amplitude of accommodation before intake of fresh palm wine was 12.16(±3.66) and mean value 30 minutes, 60 minutes and 90 minutes after intake of fresh palm wine were 13.86(±3.31), 10.19(±2.47) and 9.16(±2.12) respectively. The result obtained was statistically significant using one way ANOVA at 95% confidence interval and 0.05 level of significance; P(0.00) ˂0.05. The mean difference was significant at the 0.05 level. This study showed that fresh palm wine interfered with visual functions as increased pupil size and changes in AA were observed. Key words: Fresh palm wine, pupil diameter, amplitude of accommodation.

Some weighted quadrature methods based upon the mean value theorems

2020 ◽  
Author(s):  
Herbert H. H. Homeier ◽  
Hari M. Srivastava ◽  
Mohammad Masjed‐Jamei ◽  
Zahra Moalemi
Keyword(s):  
Mean Value ◽  
Mean Value Theorems ◽  
Quadrature Methods ◽  
The Mean ◽  
Weighted Quadrature

Mean value theorems for polynomial solutions of linear elliptic equations with constant coefficients in the complex plane

2020 ◽  
Vol 17 (4) ◽  
pp. 594-600
Author(s):  
Olga Trofymenko
Keyword(s):  
Elliptic Equation ◽  
Complex Plane ◽  
Elliptic Equations ◽  
Regular Polygon ◽  
Mean Value ◽  
Linear Elliptic Equation ◽  
Mean Value Theorems ◽  
Polynomial Solutions ◽  
Constant Coefficients ◽  
The Mean

We characterize solutions of the mean value linear elliptic equation with constant coefficients in the complex plane in the case of regular polygon.

71. The Mean Value Theorems

1961 ◽  
Vol 45 (352) ◽  
pp. 141 ◽  
Author(s):  
A. J. Moakes
Keyword(s):  
Mean Value ◽  
Mean Value Theorems ◽  
The Mean

scholarly journals Solving Higher-Order Fractional Differential Equations by the Fuzzy Generalized Conformable Derivatives

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Atimad Harir ◽  
Said Melliani ◽  
Lalla Saadia Chadli
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Higher Order ◽  
Conformable Derivatives ◽  
Fuzzy Solution ◽  
Fractional Differential ◽  
Derivatives Of

In this paper, the generalized concept of conformable fractional derivatives of order q ∈ n , n + 1 for fuzzy functions is introduced. We presented the definition and proved properties and theorems of these derivatives. The fuzzy conformable fractional differential equations and the properties of the fuzzy solution are investigated, developed, and proved. Some examples are provided for both the new solutions.

Sign in / Sign up

Export Citation Format

Share Document