Finding a General Solution to a Degenerate Equation with a Fractional Derivative
B.Yu.Irgashev
TL;DR
This paper develops a general solution for a degenerate differential equation involving a generalized Hilfer fractional derivative, utilizing special functions and providing representations for initial value problems.
Contribution
It introduces a comprehensive method to solve degenerate equations with Hilfer derivatives, including explicit solutions via Kilbas-Saigo functions.
Findings
Constructed a general solution for the degenerate Hilfer derivative equation.
Presented particular solutions using Kilbas-Saigo functions.
Derived a representation for the initial value problem.
Abstract
In the article, a general solution of an equation with a generalized Hilfer derivative, which has a degeneration, is constructed. Particular solutions are presented through the Kilbas-Saigo function. A representation of the solution of the initial problem of the type of the Cauchy problem is obtained.
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Taxonomy
TopicsDifferential Equations and Boundary Problems · Differential Equations and Numerical Methods · Advanced Computational Techniques in Science and Engineering