Existence and Approximate Controllability for Higher-Order Hilfer Fractional Evolution Equations via Fixed-Point and Sequence Approaches

Marimuthu Mohan Raja, Chan-Ho Han () and Kalyana Chakravarthy Veluvolu ()
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Marimuthu Mohan Raja: School of Electronics Engineering, Kyungpook National University, Daegu 41566, Republic of Korea
Chan-Ho Han: School of Electronics Engineering, Kyungpook National University, Daegu 41566, Republic of Korea
Kalyana Chakravarthy Veluvolu: School of Electronics Engineering, Kyungpook National University, Daegu 41566, Republic of Korea

Mathematics, 2025, vol. 13, issue 23, 1-17

Abstract: This study addresses the existence and approximate controllability of a type of higher-order Hilfer fractional evolution differential (HOHFED) system with time delays in Banach spaces. Using the properties of the Mittag–Leffler function, cosine families, and Hilfer-type fractional differential operators, we first demonstrate the existence and uniqueness of mild solutions using a fixed-point method. Furthermore, a sequential technique is proposed to establish adequate conditions for approximate controllability. A detailed example is provided to illustrate the applicability and effectiveness of the theoretical results.

Keywords: Hilfer fractional derivative; approximate controllability; mild solutions; cosine operators; fixed point approach (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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