Bernoulli-Type Spectral Numerical Scheme for Initial and Boundary Value Problems with Variable Order-Reference-Cited by-同舟云学术

Bernoulli-Type Spectral Numerical Scheme for Initial and Boundary Value Problems with Variable Order

Published:2023-05-09 Issue:5 Volume:7 Page:392
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Khan Zareen A.¹^ORCID,Ahmad Sajjad²,Zeb Salman²^ORCID,Alrabaiah Hussam³⁴^ORCID

Affiliation:

1. Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

2. Department of Mathematics, University of Malakand, Dir (L), Khyber Pakhtunkhawa, Chakdara P.O. Box 18800, Pakistan

3. College of Engineering, Al Ain University, Al Ain P.O. Box 64141, United Arab Emirates

4. Department of Mathematics, Tafila Technical University, Tafila P.O. Box 66110, Jordan

Abstract

This manuscript is devoted to using Bernoulli polynomials to establish a new spectral method for computing the approximate solutions of initial and boundary value problems of variable-order fractional differential equations. With the help of the aforementioned method, some operational matrices of variable-order integration and differentiation are developed. With the aid of these operational matrices, the considered problems are converted to algebraic-type equations, which can be easily solved using computational software. Various examples are solved by applying the method described above, and their graphical presentation and accuracy performance are provided.

Funder

Princess Nourah bint Abdulrahman University

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Link

https://www.mdpi.com/2504-3110/7/5/392/pdf

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