Predictor–corrector for non-linear differential and integral equation with fractal–fractional operators

Fractal–fractional differential and integral operators have been recognized recently as superior operators as they are able to depict physical problem with both memory effect and self-similar properties. Therefore, differential and integral equations constructed from these new operators are of great...

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Bibliographic Details
Published in:Engineering with computers Vol. 37; no. 3; pp. 2359 - 2368
Main Authors: Mekkaoui, Toufik, Atangana, Abdon, Araz, Seda İğret
Format: Journal Article
Language:English
Published: London Springer London 01.07.2021
Springer Nature B.V
Subjects:
CAE) and Design
Calculus of Variations and Optimal Control; Optimization
Classical Mechanics
Computer Science
Computer-Aided Engineering (CAD
Control
Differential equations
Fractals
Integral equations
Math. Applications in Chemistry
Mathematical analysis
Mathematical and Computational Engineering
Operators (mathematics)
Original Article
Predictor-corrector methods
Self-similarity
Systems Theory
Non-linear equations
Fractal–fractional derivative
Predictor–corrector
Fractal–fractional integral
ISSN:0177-0667, 1435-5663
Online Access:Get full text
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Summary:Fractal–fractional differential and integral operators have been recognized recently as superior operators as they are able to depict physical problem with both memory effect and self-similar properties. Therefore, differential and integral equations constructed from these new operators are of great importance. In this paper, we extend the method of predictor–corrector to obtain numerical solution of non-linear differential and integral equations. Some examples are presented to illustrate the efficiency of the new method for solving these new equations.
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ISSN:0177-0667
1435-5663
DOI:10.1007/s00366-020-00948-6