Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Second Derivatives and Laplace Operator01:22

Second Derivatives and Laplace Operator

1.4K
The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
Consider a scalar function. The curl of its...
1.4K
Definition of Laplace Transform01:22

Definition of Laplace Transform

2.5K
The Laplace transform is an indispensable mathematical technique for simplifying the resolution of differential equations by converting them into more manageable algebraic expressions. The Laplace transform of a function is denoted by L[x(t)], where x(t) is the time-domain function. The laplace transform is mathematically expressed as
2.5K
Properties of Laplace Transform-II01:16

Properties of Laplace Transform-II

262
Time differentiation, convolution, integration, and periodicity are fundamental concepts in analyzing functions and signals over time. Each concept provides a unique perspective on how functions evolve, interact, and repeat, offering essential tools for various scientific and engineering applications.
Time differentiation involves analyzing the rate of change of a function over time. Mathematically, it is the derivative of a function with respect to time. This concept can be likened to tracking...
262
Properties of Laplace Transform-I01:15

Properties of Laplace Transform-I

515
The Laplace transform is a powerful mathematical tool used to convert functions from the time domain into the frequency domain, greatly simplifying the analysis and solution of linear time-invariant systems. This transformation is facilitated by several universal properties: Linearity, Time-Scaling, Time-Shifting, and Frequency Shifting.
The Linearity property is foundational to the Laplace transform. It states that the transform of a linear combination of functions is equivalent to the same...
515
Second Order systems II01:18

Second Order systems II

144
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
144
First Order Systems01:21

First Order Systems

143
First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
143

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Retraction notice to "Molecular targets for the management of cancer using Curcuma longa Linn. phytoconstituents: A Review" [Biomedicine & Pharmacotherapy 135 (2021) 111078].

Biomedicine & pharmacotherapy = Biomedecine & pharmacotherapie·2026
Same author

Non-ICANS Neurologic Events in Patients With Relapsed/Refractory Multiple Myeloma Treated With Ciltacabtagene Autoleucel: Clinical Presentation and Management in CARTITUDE Studies.

Clinical lymphoma, myeloma & leukemia·2026
Same author

In vitro and in vivo investigations of antibacterial B-TCP/polymer composite enhanced with strontium for bone grafting and photocatalytic applications.

Cytotechnology·2026
Same author

Multi-criteria consensus-based group decision making with prospect-regret TOPSIS for human-AI tool selection under linguistic Z-numbers.

Scientific reports·2026
Same author

Three-way multi-criteria decision-making with linguistic information using prospect-regret theory and generalised TODIM for heart failure data analysis.

Scientific reports·2026
Same author

Duckworth-Lewis-Stern modeling with fuzzy logic and contextual indices for target revision in cricket.

Scientific reports·2026

Related Experiment Video

Updated: Aug 14, 2025

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

1.7K

Analysis on determining the solution of fourth-order fuzzy initial value problem with Laplace operator.

Muhammad Akram1, Tayyaba Ihsan1, Tofigh Allahviranloo2

  • 1Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan.

Mathematical Biosciences and Engineering : MBE
|January 19, 2023
PubMed
Summary

This research introduces a novel analytical method for solving fourth-order fuzzy ordinary differential equations (FODEs) using the fuzzy Laplace transform under SGH-differentiability. The method is applied to Resistance-Inductance circuits, providing a graphical analysis of the fuzzy initial value problem (FIVP) solutions.

Keywords:
Mittag-Leffler functionSGH-differentiabilityfuzzy Laplace transformfuzzy initial-value problemfuzzy number

More Related Videos

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
09:01

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

Published on: April 4, 2017

8.7K
Quantification of Global Diastolic Function by Kinematic Modeling-based Analysis of Transmitral Flow via the Parametrized Diastolic Filling Formalism
11:04

Quantification of Global Diastolic Function by Kinematic Modeling-based Analysis of Transmitral Flow via the Parametrized Diastolic Filling Formalism

Published on: September 1, 2014

11.2K

Related Experiment Videos

Last Updated: Aug 14, 2025

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

1.7K
Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
09:01

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

Published on: April 4, 2017

8.7K
Quantification of Global Diastolic Function by Kinematic Modeling-based Analysis of Transmitral Flow via the Parametrized Diastolic Filling Formalism
11:04

Quantification of Global Diastolic Function by Kinematic Modeling-based Analysis of Transmitral Flow via the Parametrized Diastolic Filling Formalism

Published on: September 1, 2014

11.2K

Area of Science:

  • Mathematics
  • Applied Mathematics
  • Numerical Analysis

Background:

  • Fuzzy initial value problems (FIVPs) are crucial in modeling uncertainty.
  • Fourth-order fuzzy ordinary differential equations (FODEs) present significant analytical challenges.
  • Existing methods for solving FIVPs of higher-order ODEs are limited.

Purpose of the Study:

  • To develop a novel analytical method for solving FIVPs of fourth-order FODEs.
  • To utilize the fuzzy Laplace transform under strongly generalized Hukuhara differentiability (SGH-differentiability).
  • To demonstrate the method's applicability through a Resistance-Inductance (RL) circuit example.

Main Methods:

  • Introduction of the fourth-order derivative of a fuzzy-valued function (FVF) under SGH-differentiability.
  • Establishment of relationships between the fourth-order derivative of FVF and its Laplace transform.
  • Development and proof of theorems concerning the Laplace transform of the fourth-order derivative of FVF.

Main Results:

  • A detailed method for solving FIVPs using the fuzzy Laplace transform is presented.
  • The proposed method is successfully applied to an RL circuit.
  • Theoretical results are supported by graphical analysis of the FIVP solutions.

Conclusions:

  • The developed analytical method effectively solves fourth-order FIVPs using the fuzzy Laplace transform.
  • The SGH-differentiability framework provides a robust approach for handling these problems.
  • The RL circuit application validates the practical utility and accuracy of the proposed technique.