Singular Cauchy Problem for a Nonlinear Fractional Differential Equation

Victor Orlov ()
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Victor Orlov: Institute of Digital Technologies and Modeling in Construction, Moscow State University of Civil Engineering, Yaroslavskoye Shosse, 26, 129337 Moscow, Russia

Mathematics, 2024, vol. 12, issue 22, 1-12

Abstract: The paper studies a nonlinear equation including both fractional and ordinary derivatives. The singular Cauchy problem is considered. The theorem of the existence of uniqueness of a solution in the neighborhood of a fixed singular point of algebraic type is proved. An analytical approximate solution is built, an a priori estimate is obtained. A formula for calculating the area where the proven theorem works is obtained. The theoretical results are confirmed by a numerical experiment in both digital and graphical versions. The technology of optimizing an a priori error using an a posteriori error is demonstrated.

Keywords: nonlinear differential equation; fractional derivative; singular points; analytical approximate solution; a priori estimate (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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