The fractional d'Alembert's formulas
Cheng-Gang Li, Miao Li, Sergey Piskarev, Mark M. Meerschaert
TL;DR
This paper extends d'Alembert's formulas to fractional integro-differential and differential equations on Banach spaces, providing new solutions, examples, and probabilistic interpretations for these advanced mathematical models.
Contribution
It introduces generalized d'Alembert's formulas for fractional equations on Banach spaces, including telegraph equations, with illustrative examples and probability interpretations.
Findings
Derived generalized d'Alembert's formulas for fractional equations
Provided examples illustrating the abstract results
Offered probabilistic interpretations of the formulas
Abstract
In this paper we develop generalized d'Alembert's formulas for abstract fractional integro-differential equations and fractional differential equations on Banach spaces. Some examples are given to illustrate our abstract results, and the probability interpretation of these fractional d'Alembert's formulas are also given. Moreover, we also provide d'Alembert's formulas for abstract fractional telegraph equations.
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Taxonomy
TopicsFractional Differential Equations Solutions · Nonlinear Differential Equations Analysis · Mathematical functions and polynomials