Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Study of a nonlinear multi-terms boundary value problem of fractional pantograph differential equations
View through CrossRef
AbstractIn this research work, a class of multi-term fractional pantograph differential equations (FODEs) subject to antiperiodic boundary conditions (APBCs) is considered. The ensuing problem involves proportional type delay terms and constitutes a subclass of delay differential equations known as pantograph. On using fixed point theorems due to Banach and Schaefer, some sufficient conditions are developed for the existence and uniqueness of the solution to the problem under investigation. Furthermore, due to the significance of stability analysis from a numerical and optimization point of view Ulam type stability and its various forms are studied. Here we mention different forms of stability: Hyers–Ulam (HU), generalized Hyers–Ulam (GHU), Hyers–Ulam Rassias (HUR) and generalized Hyers–Ulam–Rassias (GHUR). After the demonstration of our results, some pertinent examples are given.
Springer Science and Business Media LLC
Title: Study of a nonlinear multi-terms boundary value problem of fractional pantograph differential equations
Description:
AbstractIn this research work, a class of multi-term fractional pantograph differential equations (FODEs) subject to antiperiodic boundary conditions (APBCs) is considered.
The ensuing problem involves proportional type delay terms and constitutes a subclass of delay differential equations known as pantograph.
On using fixed point theorems due to Banach and Schaefer, some sufficient conditions are developed for the existence and uniqueness of the solution to the problem under investigation.
Furthermore, due to the significance of stability analysis from a numerical and optimization point of view Ulam type stability and its various forms are studied.
Here we mention different forms of stability: Hyers–Ulam (HU), generalized Hyers–Ulam (GHU), Hyers–Ulam Rassias (HUR) and generalized Hyers–Ulam–Rassias (GHUR).
After the demonstration of our results, some pertinent examples are given.
Related Results
Solving Undamped and Damped Fractional Oscillators via Integral Rohit Transform
Solving Undamped and Damped Fractional Oscillators via Integral Rohit Transform
Background: The dynamics of fractional oscillators are generally described by fractional differential equations, which include the fractional derivative of the Caputo or Riemann-Li...
Health management system for the pantographs of tilting trains
Health management system for the pantographs of tilting trains
Tilting trains are provided with the ability of rotating their carbodies of several degrees with respect to the bogies about the longitudinal axis of the train. This permits a trai...
Research on Structural reliability and reliability sensitivity of EMU pantograph
Research on Structural reliability and reliability sensitivity of EMU pantograph
Abstract
Due to the uncertainty of the contact state between the pantograph and the power grid when the EMU is running at high speed, as well as the influence of roa...
Soham Transform in Fractional Differential Equations
Soham Transform in Fractional Differential Equations
Objectives: Soham transforms is one of the appropriate tools for solving fractional differential equations that are flexible enough to adapt to different purposes. Methods: Integra...
Collocation Method Based on Genocchi Operational Matrix for Solving Generalized Fractional Pantograph Equations
Collocation Method Based on Genocchi Operational Matrix for Solving Generalized Fractional Pantograph Equations
An effective collocation method based on Genocchi operational matrix for solving generalized fractional pantograph equations with initial and boundary conditions is presented. Usin...
Balanced Force Pantograph and OCS
Balanced Force Pantograph and OCS
At the core of electrified railroad design is the Pantograph and Overhead Contact System (OCS). The design of the OCS has been essentially unchanged for nearly 100 years. The panto...
On α-Fractional Bregman Divergence to study α-Fractional Minty’s Lemma
On α-Fractional Bregman Divergence to study α-Fractional Minty’s Lemma
In this paper fractional variational inequality problems (FVIP) and dual fractional variational inequality problems (DFVIP), Fractional minimization problems are defined with the h...
Simulation analysis of offline characteristics between pantograph and catenary
Simulation analysis of offline characteristics between pantograph and catenary
To study the offline characteristics of pantograph‐catenary, finite element method was adopted in this study, and the coupled model of pantograph and catenary was established in th...