Existence of optimal pairs and solvability of non-autonomous fractional Sobolev-type integrodifferential equations

Madhukant Sharma ()
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Madhukant Sharma: Dhirubhai Ambani Institute of Information and Communication Technology

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 1, 1-12

Abstract: Abstract This article establishes a sufficient criteria for the existence of an optimal pair and a mild-solution of a non-autonomous fractional Sobolev-type integro-differential equation (FSIDE) with a generalized nonlocal condition. The fixed-point technique, tools from fractional calculus and the semigroup-theory played a valuable role in deriving the results. It is imperative to mention the distinguish attributes of this work that the developed results don’t assume (i) that the generated semigroup is compact; (ii) that the linear operators $$-S(t)$$ - S ( t ) are bounded; and (iii) that the operator D is strongly continuous. We also provide an example to demonstrate the established results.

Keywords: Sobolev-type equations; Fractional differential equations; Fractional optimal control problems; Integro-differential systems; 26A33; 34K37; 35R09; 49J20 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-023-00457-4

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