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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 54 Issue: 4

Existence and stability analysis for $\Phi$-Caputo generalized proportional fractional differential Langevin equation

Hamid Lmou(Sultan Moulay Slimane)0000-0002-8786-2230
Khalid Hilal(Sultan Moulay Slimane)0000-0002-0806-2623
Ahmed Kajounı(Sultan Moulay Slimane)0000-0001-8484-6107
Pages
—
Publication Date
2025-08-29
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

As an application, we provide an example to illustrate our theoretical result.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This paper aims to investigate the existence, uniqueness and stability results for a new class of $\Phi$-Caputo generalized proportional fractional $(\mathsf{GPF})$ differential Langevin equation.
📊
Key Findings & Data:We present and discuss some of the characteristics of the generalized proportional fractional derivative which can be considered as generalization and modification of the fractional conformable derivative by generating $\Phi$-Caputo generalized proportional fractional derivatives involving exponential functions in it's kernel also this kind of fractional derivative generalize the well-known fractional derivatives, for different values of function $\Phi$.
💡
Conclusion & Impact:As an application, we provide an example to illustrate our theoretical result.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:$\Phi$-Caputo generalized proportional fractional derivative · $\Phi$-Caputo fractional differential Langevin equations · fixed point theorems

Abstract

This paper aims to investigate the existence, uniqueness and stability results for a new class of $\Phi$-Caputo generalized proportional fractional $(\mathsf{GPF})$ differential Langevin equation. We present and discuss some of the characteristics of the generalized proportional fractional derivative which can be considered as generalization and modification of the fractional conformable derivative by generating $\Phi$-Caputo generalized proportional fractional derivatives involving exponential functions in it's kernel also this kind of fractional derivative generalize the well-known fractional derivatives, for different values of function $\Phi$. Utilizing Krasnoselskii's fixed point theorem and the Banach contraction principle, we established results on existence and uniqueness, we also examine various types of stability, including Ulam-Hyers stability and generalized Ulam-Hyers stability. As an application, we provide an example to illustrate our theoretical result.

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Cite This Article

Lmou, H., Hilal, K., Kajounı, A. (2025). Existence and stability analysis for $\Phi$-Caputo generalized proportional fractional differential Langevin equation. Hacettepe Journal of Mathematics and Statistics, Volume: 54 Issue: 4. https://doi.org/10.15672/hujms.1487219

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