MODULI OF CONTINUITY FOR FUNCTIONS IN SOBOLEV SPACES AND HAAR WAVELET SOLUTIONS TO FRACTIONAL BASSET EQUATION

Shyam Lal; Abhilasha *

MODULI OF CONTINUITY FOR FUNCTIONS IN SOBOLEV SPACES AND HAAR WAVELET SOLUTIONS TO FRACTIONAL BASSET EQUATION

Abstract

In this paper, the method for solving fractional differential equations have been proposed using the Haar wavelet operational matrix of fractional integration. An operational matrix of fractional integration using the Haar wavelet is designed to solve a linear multi-term fractional differential equation as well as a system of fractional differential equations. The Basset equation for different fractional orders and a system of fractional differential equations both have been solved in order to validate and show the viability of the proposed method. Furthermore, it has also been demonstrated to approximate functions in Sobolev space via the Haar wavelet approach with the help of moduli of continuity. By treating fractional differential equations as a set of algebraic equations, this study significantly advances both the moduli of continuity and numerical solutions of fractional differential equations.

Keywords

Thanks

Shyam Lal, one of the authors, likes to extend his gratitude to DST-CIMS for encouragement to this work. The authors thank the reviewer for his valuable and insightful comments which have significantly enhance the paper.

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Details

Primary Language

English

Subjects

Numerical Solution of Differential and Integral Equations, Lie Groups, Harmonic and Fourier Analysis, Operator Algebras and Functional Analysis

Journal Section

Research Article

Authors

Shyam Lal
0000-0001-8598-2207
India

Abhilasha * ^* This is me
0000-0012-3456-789X
India

Publication Date

June 9, 2026

Submission Date

April 9, 2025

Acceptance Date

September 9, 2025

Published in Issue

Year 2026 Volume: 16 Number: 6

IZ

https://izlik.org/JA83YM52AX

Cite

RIS / Bibtex

APA

Lal, S., & *, A. (2026). MODULI OF CONTINUITY FOR FUNCTIONS IN SOBOLEV SPACES AND HAAR WAVELET SOLUTIONS TO FRACTIONAL BASSET EQUATION. TWMS Journal of Applied and Engineering Mathematics, 16(6), 696-712. https://izlik.org/JA83YM52AX

AMA

1.Lal S, * A. MODULI OF CONTINUITY FOR FUNCTIONS IN SOBOLEV SPACES AND HAAR WAVELET SOLUTIONS TO FRACTIONAL BASSET EQUATION. JAEM. 2026;16(6):696-712. https://izlik.org/JA83YM52AX

Chicago

Lal, Shyam, and Abhilasha *. 2026. “MODULI OF CONTINUITY FOR FUNCTIONS IN SOBOLEV SPACES AND HAAR WAVELET SOLUTIONS TO FRACTIONAL BASSET EQUATION”. TWMS Journal of Applied and Engineering Mathematics 16 (6): 696-712. https://izlik.org/JA83YM52AX.

EndNote

Lal S, * A (June 1, 2026) MODULI OF CONTINUITY FOR FUNCTIONS IN SOBOLEV SPACES AND HAAR WAVELET SOLUTIONS TO FRACTIONAL BASSET EQUATION. TWMS Journal of Applied and Engineering Mathematics 16 6 696–712.

IEEE

[1]S. Lal and A. *, “MODULI OF CONTINUITY FOR FUNCTIONS IN SOBOLEV SPACES AND HAAR WAVELET SOLUTIONS TO FRACTIONAL BASSET EQUATION”, JAEM, vol. 16, no. 6, pp. 696–712, June 2026, [Online]. Available: https://izlik.org/JA83YM52AX

ISNAD

Lal, Shyam - *, Abhilasha. “MODULI OF CONTINUITY FOR FUNCTIONS IN SOBOLEV SPACES AND HAAR WAVELET SOLUTIONS TO FRACTIONAL BASSET EQUATION”. TWMS Journal of Applied and Engineering Mathematics 16/6 (June 1, 2026): 696-712. https://izlik.org/JA83YM52AX.

JAMA

1.Lal S, * A. MODULI OF CONTINUITY FOR FUNCTIONS IN SOBOLEV SPACES AND HAAR WAVELET SOLUTIONS TO FRACTIONAL BASSET EQUATION. JAEM. 2026;16:696–712.

MLA

Lal, Shyam, and Abhilasha *. “MODULI OF CONTINUITY FOR FUNCTIONS IN SOBOLEV SPACES AND HAAR WAVELET SOLUTIONS TO FRACTIONAL BASSET EQUATION”. TWMS Journal of Applied and Engineering Mathematics, vol. 16, no. 6, June 2026, pp. 696-12, https://izlik.org/JA83YM52AX.

Vancouver

1.Shyam Lal, Abhilasha *. MODULI OF CONTINUITY FOR FUNCTIONS IN SOBOLEV SPACES AND HAAR WAVELET SOLUTIONS TO FRACTIONAL BASSET EQUATION. JAEM [Internet]. 2026 Jun. 1;16(6):696-712. Available from: https://izlik.org/JA83YM52AX