A generalized Legendre transform method and its applications

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-03-25 DOI:10.1016/j.cam.2025.116646

Imtiaz Waheed, Mujeeb ur Rehman

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引用次数: 0

Abstract

The article aims to develop the shifted Legendre transform method in the context of

Ψ

-fractional calculus, termed as the

Ψ

-shifted Legendre transform. The proposed transform method generalizes the classical Legendre transform. The

Ψ

-shifted Legendre transform is applied to differential and integral operators. Moreover, the inverse operator, various operational properties of

Ψ

-shifted Legendre polynomials, and the

Ψ

-shifted transform method are investigated. The convolution for the

Ψ

-shifted Legendre transform in the framework of

Ψ

-fractional calculus is also determined. Finally, fractional differential equations involving the

Ψ

-fractional derivative are solved using the

Ψ

-shifted Legendre transform method.

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.