Solvability of Multi-Order $\psi$-Hilfer Fractional Langevin Equations with Infinite Delay in Weighted Phase Spaces

Abdelatif Boutiara; Mohammed S Abdo

doi:10.32323/ujma.1768066

Solvability of Multi-Order $\psi$-Hilfer Fractional Langevin Equations with Infinite Delay in Weighted Phase Spaces

Abstract

This work introduces a new class of fractional Langevin equations with infinite delay by incorporating generalized Hilfer derivatives within a weighted Banach space framework. Unlike existing studies that rely on standard Caputo or Hilfer operators without incorporating delay-weight interactions, the proposed formulation simultaneously accounts for nonlocal memory and non-uniform decay effects. This dual mechanism enables the modeling of long-term hereditary responses in systems where past states contribute with varying intensity over time, a behavior unattainable in traditional fractional models. Existence and uniqueness of solutions are established using Banach's fixed point theorem and the Leray--Schauder alternative, both adapted to the weighted setting. Two illustrative examples are provided to demonstrate how generalized weighted Hilfer derivatives alter the dynamical behavior compared to classical formulations. These results offer a new perspective on delayed fractional systems, expanding the analytical toolkit available for modeling complex memory-driven processes.

Keywords

$\psi$-Hilfer fractional operator, Fixed point theorem, Infinite delay, Langevin equation, Phase space

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Details

Primary Language

English

Subjects

Numerical Solution of Differential and Integral Equations, Partial Differential Equations

Journal Section

Research Article

Authors

Abdelatif Boutiara ^*
0000-0002-6032-4694
Algeria

Mohammed S Abdo
0000-0001-9085-324X
Yemen

Early Pub Date

January 11, 2026

Publication Date

January 11, 2026

Submission Date

August 18, 2025

Acceptance Date

November 27, 2025

Published in Issue

Year 2026 Volume: 9 Number: 1

DOI

https://doi.org/10.32323/ujma.1768066

IZ

https://izlik.org/JA28FM27XB

APA

Boutiara, A., & Abdo, M. S. (2026). Solvability of Multi-Order $\psi$-Hilfer Fractional Langevin Equations with Infinite Delay in Weighted Phase Spaces. Universal Journal of Mathematics and Applications, 9(1), 19-31. https://doi.org/10.32323/ujma.1768066

AMA

1.Boutiara A, Abdo MS. Solvability of Multi-Order $\psi$-Hilfer Fractional Langevin Equations with Infinite Delay in Weighted Phase Spaces. Univ. J. Math. Appl. 2026;9(1):19-31. doi:10.32323/ujma.1768066

Chicago

Boutiara, Abdelatif, and Mohammed S Abdo. 2026. “Solvability of Multi-Order $\psi$-Hilfer Fractional Langevin Equations With Infinite Delay in Weighted Phase Spaces”. Universal Journal of Mathematics and Applications 9 (1): 19-31. https://doi.org/10.32323/ujma.1768066.

EndNote

Boutiara A, Abdo MS (March 1, 2026) Solvability of Multi-Order $\psi$-Hilfer Fractional Langevin Equations with Infinite Delay in Weighted Phase Spaces. Universal Journal of Mathematics and Applications 9 1 19–31.

IEEE

[1]A. Boutiara and M. S. Abdo, “Solvability of Multi-Order $\psi$-Hilfer Fractional Langevin Equations with Infinite Delay in Weighted Phase Spaces”, Univ. J. Math. Appl., vol. 9, no. 1, pp. 19–31, Mar. 2026, doi: 10.32323/ujma.1768066.

ISNAD

Boutiara, Abdelatif - Abdo, Mohammed S. “Solvability of Multi-Order $\psi$-Hilfer Fractional Langevin Equations With Infinite Delay in Weighted Phase Spaces”. Universal Journal of Mathematics and Applications 9/1 (March 1, 2026): 19-31. https://doi.org/10.32323/ujma.1768066.

JAMA

1.Boutiara A, Abdo MS. Solvability of Multi-Order $\psi$-Hilfer Fractional Langevin Equations with Infinite Delay in Weighted Phase Spaces. Univ. J. Math. Appl. 2026;9:19–31.

MLA

Boutiara, Abdelatif, and Mohammed S Abdo. “Solvability of Multi-Order $\psi$-Hilfer Fractional Langevin Equations With Infinite Delay in Weighted Phase Spaces”. Universal Journal of Mathematics and Applications, vol. 9, no. 1, Mar. 2026, pp. 19-31, doi:10.32323/ujma.1768066.

Vancouver

1.Abdelatif Boutiara, Mohammed S Abdo. Solvability of Multi-Order $\psi$-Hilfer Fractional Langevin Equations with Infinite Delay in Weighted Phase Spaces. Univ. J. Math. Appl. 2026 Mar. 1;9(1):19-31. doi:10.32323/ujma.1768066