Representation of a solution to a class of linear discrete Langevin equations

Mustafa Aydin; Mustafa Aydin

doi:10.3934/era.2026156

Electronic Research Archive

2026, Volume 34, Issue 5: 3503-3515. doi: 10.3934/era.2026156

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Representation of a solution to a class of linear discrete Langevin equations

Mustafa Aydin ^,

Muradiye Vocational School, Van Yuzuncu Yil University, Tuşba 65080, Van, Türkiye

Received: 13 February 2026 Revised: 25 March 2026 Accepted: 10 April 2026 Published: 22 April 2026

This paper introduced, for the first time, a novel discrete Langevin equation as a new generalization of the classical Langevin model, involving two distinct integer-order differences. A new special function generated by the system parameters was defined to obtain explicit analytical solutions of the associated initial value problem. Several special cases were discussed, and open problems were proposed. The results established a new theoretical framework for discrete Langevin-type systems and contributed to the qualitative theory of difference equations.
- discrete Langevin equation,
- novel discrete exponential,
- representation of solutions
Citation: Mustafa Aydin. Representation of a solution to a class of linear discrete Langevin equations[J]. Electronic Research Archive, 2026, 34(5): 3503-3515. doi: 10.3934/era.2026156

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Abstract

This paper introduced, for the first time, a novel discrete Langevin equation as a new generalization of the classical Langevin model, involving two distinct integer-order differences. A new special function generated by the system parameters was defined to obtain explicit analytical solutions of the associated initial value problem. Several special cases were discussed, and open problems were proposed. The results established a new theoretical framework for discrete Langevin-type systems and contributed to the qualitative theory of difference equations.

References

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