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pith:6R2FRXKC

pith:2026:6R2FRXKC4WK6LXMLFAM35ZBEWA

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Lie symmetry classification and invariant solutions of time-fractional telegraph systems with variable coefficients

Bayarmagnai Gombodorj, Bayarpurev Mongol, Khongorzul Dorjgotov, Sodbaatar Adiya, Uuganbayar Zunderiya

Time-fractional telegraph systems with variable coefficients fall into three symmetry classes determined by the relation between transport and potential terms.

arxiv:2604.25079 v1 · 2026-04-28 · math-ph · math.MP

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Claims

C1strongest claim

We establish a complete Lie group classification for sufficiently differentiable coefficient functions and determine all functional forms that admit such symmetry extensions. The symmetry structure is shown to depend fundamentally on the relationship between the transport coefficient and the potential function, resulting in three distinct symmetry classes. For each case, optimal systems of one-dimensional Lie subalgebras are constructed, and the governing fractional partial differential equations are systematically reduced to fractional ordinary differential equations. Exact invariant solutions are obtained in closed form and expressed in terms of Mittag-Leffler functions, generalized Wright functions, and Fox H-functions.

C2weakest assumption

The coefficient functions are sufficiently differentiable and the Riemann-Liouville fractional derivative can be used directly for the symmetry analysis without further compatibility conditions imposed by the variable coefficients.

C3one line summary

Lie symmetry classification of time-fractional telegraph systems with variable coefficients identifies three symmetry classes depending on the relation between transport coefficient and potential, and produces exact invariant solutions in Mittag-Leffler, generalized Wright, and Fox H-functions.

References

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[1] A stochastic model related to the telegrapher’s equation.Rocky Mountain Journal of Math- ematics, 4(3):497–509 1974

[2] Time-fractional telegraph equations and telegraph processes with brownian time.Probability Theory and Related Fields, 128(1):141–160 2004

[3] George Bluman, Temuerchaolu, and R. Sahadevan. Local and nonlocal symmetries for nonlinear tele- graph equations.Journal of Mathematical Physics, 46(2):023505, 2005 2005

[4] Conservation laws for nonlinear telegraph equations.Journal of Mathematical Analysis and Applications, 310(2):459–476 2005

[5] Comparing symmetries and conservation laws of nonlinear telegraph equations.Journal of Mathematical Physics, 46(7):073513 2005

Receipt and verification

First computed	2026-06-08T01:04:05.817733Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f47458dd42e595e5dd8b2819bee424b0226d0310af44b8594adc402d49ecf6b5

Aliases

arxiv: 2604.25079 · arxiv_version: 2604.25079v1 · doi: 10.48550/arxiv.2604.25079 · pith_short_12: 6R2FRXKC4WK6 · pith_short_16: 6R2FRXKC4WK6LXML · pith_short_8: 6R2FRXKC

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Canonical record JSON

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    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-04-28T00:24:11Z",
    "title_canon_sha256": "ce63116485340f369b59003fe86ac2bd3fa7d1544e450721c55107efea2a62af"
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