Analysis of Topological Degree Method for Solving Ambartsumian-Type Mathieu Fractional Differential Equations Under Φ-Hilfer Derivative

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DOI: https://doi.org/10.28924/2291-8639-24-2026-112
Published: Apr 20, 2026
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R. Vivek, R. George, Analysis of Topological Degree Method for Solving Ambartsumian-Type Mathieu Fractional Differential Equations Under Φ-Hilfer Derivative, Int. J. Anal. Appl., 24 (2026), 112.

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R. Vivek, R. George

Abstract

The Ambartsumian equation arises in astronomy and is used in the theory of surface brightness in the Milky Way. In this manuscript, we consider a new category of Ambartsumian-type Mathieu fractional differential systems involving the Φ-Hilfer fractional derivative. We study the existence and uniqueness of solutions of the above system using the topological degree method for condensing maps and Banach’s contraction principle. Furthermore, Ulam–Hyers and generalized Ulam–Hyers stability are investigated, by using the generalized Gronwall’s inequality and nonlinear analysis issue. As an application, we provide an example to illustrate the validity of our results.

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