This chapter, focused on fractional neutral integro-differential structures with state-dependent delay in Banach spaces, building from semigroups, fractional calculus and the Banach contraction principle. Our proceeding hypothesis assume that the functions defining the equation meet specific Lipschitz conditions. The fractional equations in the time domain consider derivatives in the range of \(\nu \in (0, 1)\) . Theoretical and numerical outcomes are discussed using different input terms introduced in the fractional equation. The examples are discussed for showing the application of the outcomes developed.

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Results on Existence and Controllability of Caputo Fractional Neutral Integro-Differential Equations

  • Palaniyappan Kalamani

摘要

This chapter, focused on fractional neutral integro-differential structures with state-dependent delay in Banach spaces, building from semigroups, fractional calculus and the Banach contraction principle. Our proceeding hypothesis assume that the functions defining the equation meet specific Lipschitz conditions. The fractional equations in the time domain consider derivatives in the range of \(\nu \in (0, 1)\) . Theoretical and numerical outcomes are discussed using different input terms introduced in the fractional equation. The examples are discussed for showing the application of the outcomes developed.