Fractional Conformable Stochastic Integrodifferential Equations: Existence, Uniqueness, and Numerical Simulations Utilizing the Shifted Legendre Spectral Collocation Algorithm

Theoretical and numerical studies of fractional conformable stochastic integrodifferential equations are introduced in this study. Herein, to emphasize the solution’s existence, we provide proof based on Picard iterations and Arzela−Ascoli’s theorem, whilst the proof of the uniqueness mainly depends...

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Bibliographic Details
Published in:Mathematical problems in engineering 2022-11, Vol.2022, p.1-21
Main Authors: Badawi, Haneen, Shawagfeh, Nabil, Abu Arqub, Omar
Format: Article
Language:English
Subjects:
Algorithms
Brownian motion
Calculus
Collocation
Computer simulation
Mathematical models
Mathematical tables
Mathematicians
Numerical methods
Picard iterations
Polynomials
Population growth
Random variables
Stochastic models
Uniqueness
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Summary:Theoretical and numerical studies of fractional conformable stochastic integrodifferential equations are introduced in this study. Herein, to emphasize the solution’s existence, we provide proof based on Picard iterations and Arzela−Ascoli’s theorem, whilst the proof of the uniqueness mainly depends on the famous Gronwall’s inequality. Also, we introduce the basic concepts related to shifted Legendre orthogonal polynomials which are utilized to be the basic functions of the spectral collocation algorithm to obtain approximate solutions for the mentioned equations that are not easy to be solved analytically. The substantial idea of the proposed algorithm is to transform such equations into a system containing a finite number of algebraic equations that can be treated using familiar numerical methods. For computational aims, we make a suitable discretization to evaluate the values of the Brownian motion, the noise term considered in our problem, at specific points. In addition, the feasibility and efficiency of the proposed algorithm are proved through convergence analysis and mathematical examples. To exhibit the mathematical simulation, graphs and tables are lucidly shown. Obviously, the physical interpretation of the displayed graphics accurately describes the behavior of the solutions. Despite the simplicity of the presented technique, it produces accurate and reasonable results as notarized in the conclusion section.
ISSN:1024-123X
1563-5147
DOI:10.1155/2022/5104350