scholarly journals The stability of the fractional Volterra integro‐differential equation by means of Ψ‐Hilfer operator revisited

2021 ◽  
Author(s):  
Dumitru Baleanu ◽  
Reza Saadati ◽  
José Sousa
Keyword(s):  
Differential Equation ◽  
Integro Differential Equation ◽  
The Stability

scholarly journals A Numerical Study of Nonlinear Fractional Order Partial Integro-Differential Equation with a Weakly Singular Kernel

2021 ◽  
Vol 5 (3) ◽  
pp. 85
Author(s):  
Tayyaba Akram ◽  
Zeeshan Ali ◽  
Faranak Rabiei ◽  
Kamal Shah ◽  
Poom Kumam
Keyword(s):  
Differential Equation ◽  
Fractional Order ◽  
Numerical Study ◽  
Stability And Convergence ◽  
Weakly Singular Kernel ◽  
Integro Differential Equation ◽  
Suggested Technique ◽  
Collocation Approach ◽  
The Stability ◽  
Efficiency And Reliability

Fractional differential equations can present the physical pathways with the storage and inherited properties due to the memory factor of fractional order. The purpose of this work is to interpret the collocation approach for tackling the fractional partial integro-differential equation (FPIDE) by employing the extended cubic B-spline (ECBS). To determine the time approximation, we utilize the Caputo approach. The stability and convergence analysis have also been analyzed. The efficiency and reliability of the suggested technique are demonstrated by two numerical applications, which support the theoretical results and the effectiveness of the implemented algorithm.

scholarly journals Uniform Stability In Nonlinear Infinite Delay Volterra Integro-differential Equations Using Lyapunov Functionals

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Youssef Raffoul ◽  
Habib Rai
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Exponential Stability ◽  
Lyapunov Functional ◽  
Infinite Delay ◽  
Zero Solution ◽  
Uniform Stability ◽  
Lyapunov Functionals ◽  
Integro Differential Equation ◽  
The Stability

AbstractIn [10] the first author used Lyapunov functionals and studied the exponential stability of the zero solution of finite delay Volterra Integro-differential equation. In this paper, we use modified version of the Lyapunov functional that were used in [10] to obtain criterion for the stability of the zero solution of the infinite delay nonlinear Volterra integro-differential equation

scholarly journals Semi-Hyers–Ulam–Rassias Stability of a Volterra Integro-Differential Equation of Order I with a Convolution Type Kernel via Laplace Transform

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2181
Author(s):  
Daniela Inoan ◽  
Daniela Marian
Keyword(s):  
Differential Equation ◽  
Laplace Transform ◽  
Convolution Type ◽  
Convolution Product ◽  
Polynomial Functions ◽  
Integro Differential Equation ◽  
The Laplace Transform ◽  
The Stability ◽  
Rassias Stability

In this paper, we investigate the semi-Hyers–Ulam–Rassias stability of a Volterra integro-differential equation of order I with a convolution type kernel. To this purpose the Laplace transform is used. The results obtained show that the stability holds for problems formulated with various functions: exponential and polynomial functions. An important aspect that appears in the form of the studied equation is the symmetry of the convolution product.

Some numerical graphs with successive approximation method of fractional integro–differential equation

2019 ◽  
Vol 8 (4) ◽  
pp. 36
Author(s):  
Samir H. Abbas
Keyword(s):  
Differential Equation ◽  
Successive Approximation ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
Successive Approximation Method ◽  
Integro Differential Equation

This paper studies the existence and uniqueness solution of fractional integro-differential equation, by using some numerical graphs with successive approximation method of fractional integro –differential equation. The results of written new program in Mat-Lab show that the method is very interested and efficient. Also we extend the results of Butris [3].

Normalization Bernstein Basis For Solving Fractional Fredholm-Integro Differential Equation

2018 ◽  
pp. 491
Author(s):  
Abdul Khaleq O. Al-Jubory ◽  
Shaymaa Hussain Salih
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Linear System ◽  
Differential Equations ◽  
Bernstein Basis ◽  
Traditional Methods ◽  
Integro Differential Equation

In this work, we employ a new normalization Bernstein basis for solving linear Freadholm of fractional integro-differential equations  nonhomogeneous  of the second type (LFFIDEs). We adopt Petrov-Galerkian method (PGM) to approximate solution of the (LFFIDEs) via normalization Bernstein basis that yields linear system. Some examples are given and their results are shown in tables and figures, the Petrov-Galerkian method (PGM) is very effective and convenient and overcome the difficulty of traditional methods. We solve this problem (LFFIDEs) by the assistance of Matlab10.   

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