Method of separation of variables and exact solution of time fractional nonlinear partial differential and differential-difference equations

Uma Maheswari, Chandrasekaran; Sahadevan, Ramajayam; Yogeshwaran, Munusamy

doi:10.1007/s13540-023-00199-4

Cited by 2 publications

(1 citation statement)

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“…A range of methods exist, and the mathematical structures required in investigations relating to FDEs are endless, but many methods involve transformations of some kind, either those that reduce to an integer-order equation or a reduction to one of fractional order [18][19][20][21][22]. Several notable and recent applications of FDEs can be seen in the literature: the method of separation of variables for some FDEs [23], a Zoomeron equation's solutions [24], and families of second-order numerical results were investigated [25].…”

Section: Introductionmentioning

confidence: 99%

Lie Symmetries and the Invariant Solutions of the Fractional Black–Scholes Equation under Time-Dependent Parameters

Jamal,

Champala,

Khan

2024

Fractal Fract

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In this paper, we consider the time-fractional Black–Scholes model with deterministic, time-varying coefficients. These time parametric constituents produce a model with greater flexibility that may capture empirical results from financial markets and their time-series datasets. We make use of transformations to reduce the underlying model to the classical heat transfer equation. We show that this transformation procedure is possible for a specific risk-free interest rate and volatility of stock function. Furthermore, we reverse these transformations and apply one-dimensional optimal subalgebras of the infinitesimal symmetry generators to establish invariant solutions.

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