scholarly journals A new approach for nuclear family model with fractional order Caputo derivative

2020 ◽  
Vol 5 (1) ◽  
pp. 393-404
Author(s):  
Ilknur Koca ◽  
Pelin Yaprakdal
Keyword(s):  
Applied Sciences ◽  
Mathematical Modeling ◽  
Fractional Order ◽  
Caputo Derivative ◽  
Nuclear Family ◽  
New Approach ◽  
Existence And Uniqueness Results ◽  
New Methods ◽  
Uniqueness Results ◽  
Family Model

AbstractA work on a mathematical modeling is very popular in applied sciences. Nowadays many mathematical models have been considered and new methods have been used for approaching of these models. In this paper we are considering mathematical modeling of nuclear family model with fractional order Caputo derivative. Also the existence and uniqueness results and numerical scheme are given with Adams-Bashforth scheme via fractional order Caputo derivative.

On existence and uniqueness results for iterative mixed integrodifferential equation of fractional order

2020 ◽  
Vol 26 (2) ◽  
pp. 263-272
Author(s):  
S. I. Unhale ◽  
Subhash D. Kendre
Keyword(s):  
Numerical Solution ◽  
Fractional Order ◽  
Integrodifferential Equation ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
Integrodifferential Equations ◽  
Successive Approximation Method ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

AbstractThe objective of this work is to study the local existence, uniqueness, stability and other properties of solutions of iterative mixed integrodifferential equations of fractional order. The Successive Approximation Method is applied for the numerical solution of iterative mixed integrodifferential equations of fractional order.

scholarly journals On existence and stability results for nonlinear fractional delay differential equations

2018 ◽  
Vol 36 (4) ◽  
pp. 55-75 ◽  
Author(s):  
Kishor D. Kucche ◽  
Sagar T. Sutar
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Delay Differential Equations ◽  
Successive Approximation Method ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Existence And Stability ◽  
Fractional Delay ◽  
Delay Differential ◽  
Rassias Stability

We establish existence and uniqueness results for fractional order delay differential equations. It is proved that successive approximation method can also be successfully applied to study Ulam--Hyers stability, generalized Ulam--Hyers stability, Ulam--Hyers--Rassias stability, generalized Ulam--Hyers--Rassias stability, $ \mathbb{E}_{\alpha}$--Ulam--Hyers stability and generalized $ \mathbb{E}_{\alpha}$--Ulam--Hyers stability of fractional order delay differential equations.

scholarly journals Smart Manufacturing Technology

2021 ◽  
Vol 11 (17) ◽  
pp. 8202
Author(s):  
Michele Calì
Keyword(s):  
Applied Sciences ◽  
Business Management ◽  
Manufacturing Technology ◽  
Smart Manufacturing ◽  
Research Directions ◽  
New Approach ◽  
New Methods ◽  
New Ideas ◽  
Reducing Costs ◽  
Manufacturing Technologies

This Special Issue of Applied Sciences provides a collection of original papers on smart manufacturing technology with the aim of: examining emerging aspects of digitalization in the industrial and biomedical fields, as well as in business management and sustainability; proposing and developing a new approach useful for companies, factories, and organizations to achieve greater innovation and productivity—as well as sustainability—by applying smart manufacturing technologies; and exploring new ideas and encouraging research directions so as to obtain autonomous and semiautonomous processes, high-quality products, and services with a greater integration and interconnection of resources while reducing costs. The advantages of new methods and experimental results obtained in the collected contributions are discussed promoting further design, implementation, and application in the various fields.

scholarly journals Nonlocal boundary value problems for ψ-Hilfer fractional-order Langevin equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Cholticha Nuchpong ◽  
Sotiris K. Ntouyas ◽  
Devaraj Vivek ◽  
Jessada Tariboon
Keyword(s):  
Fractional Order ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Integral Boundary Conditions ◽  
Langevin Equations ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

AbstractIn the paper, we study a boundary value problem for a class of ψ-Hilfer fractional-order Langevin equations with multi-point integral boundary conditions. Existence and uniqueness results are established by using well-known fixed point theorems. Examples illustrating the main results are also included.

scholarly journals Existence and Ulam–Hyers Stability of a Fractional-Order Coupled System in the Frame of Generalized Hilfer Derivatives

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2543
Author(s):  
Abdulkafi M. Saeed ◽  
Mohammed S. Abdo ◽  
Mdi Begum Jeelani
Keyword(s):  
Fixed Point ◽  
Fractional Order ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Coupled System ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Special Cases ◽  
Stability Of The Solution

In this research paper, we consider a class of a coupled system of fractional integrodifferential equations in the frame of Hilfer fractional derivatives with respect to another function. The existence and uniqueness results are obtained in weighted spaces by applying Schauder’s and Banach’s fixed point theorems. The results reported here are more general than those found in the literature, and some special cases are presented. Furthermore, we discuss the Ulam–Hyers stability of the solution to the proposed system. Some examples are also constructed to illustrate and validate the main results.

The continuation of solutions to systems of Caputo fractional order differential equations

2020 ◽  
Vol 23 (2) ◽  
pp. 591-599 ◽  
Author(s):  
Cong Wu ◽  
Xinzhi Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Order ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Existence And Uniqueness Results ◽  
Fractional Order Differential Equations ◽  
Uniqueness Results ◽  
Schäuder Fixed Point Theorem

AbstractIn this paper, we study the continuation of solutions to systems of Caputo fractional order differential equations. The continuation is constructed and proven by using the Schauder Fixed Point Theorem. As a necessary prerequisite to the continuation, the existence and uniqueness results generalized for systems are also reviewed.

scholarly journals On Some Existence and Uniqueness Results for a Class of Equations of Order0<α≤1on Arbitrary Time Scales

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Abdourazek Souahi ◽  
Assia Guezane-Lakoud ◽  
Rabah Khaldi
Keyword(s):  
Differential Equations ◽  
Time Scales ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solution ◽  
Arbitrary Time ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential

This paper investigates the existence and uniqueness of solution for a class of nonlinear fractional differential equations of fractional order0<α≤1in arbitrary time scales. The results are established using extensions of Krasnoselskii-Krein, Rogers, and Kooi conditions.

A New Approach to the Formation of Test Mathematical Models of Complex Electrical Circuits

2021 ◽  
Vol 64 (6) ◽  
pp. 5-11
Author(s):  
Ivan Lebedev ◽  
◽  
Nikolay Savelov ◽  
Sergey Basan ◽  
◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Initial Data ◽  
Mathematical Models ◽  
Circuit Diagram ◽  
Electrical Circuits ◽  
New Approach ◽  
New Methods ◽  
Unlimited Number ◽  
The Creation ◽  
Complex Circuits

When developing new methods for analyzing electrical circuits and comparing various already developed methods, one of the actual problems is the creation of tests for evaluating the effectiveness of algorithms. For such tests, it is advisable to use schemes of complex circuits. However, with an increase in the number of circuit elements, the development of a circuit diagram, preparation of initial data for mathematical modeling and vis-ual presentation of the circuit become more and more difficult. To solve these problems, it is proposed to use pre-ordered electrical circuits. An algorithm for the formation of mathematical models of circuits with an almost unlimited number of elements is proposed. Experiments on the formation and application of mathematical models of electrical circuits containing more than five hundred elements have been carried out. The generated mathematical models are used to evaluate a specific algorithm for analyzing electrical circuits.

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