Abstract
We prove a theorem on the existence and uniqueness of a solution as well as on a sensitivity (i.e., differentiable dependence of a solution on a functional parameter) of a fractional integrodifferential Cauchy problem of Volterra type. The proof of this result is based on a theorem on diffeomorphism between Banach and Hilbert spaces. The main assumption is the Palais-Smale condition.
Highlights
We prove a theorem on the existence and uniqueness of a solution as well as on a sensitivity of a fractional integrodifferential Cauchy problem of Volterra type
Integrodifferential systems are investigated in finite and infinite dimensional spaces, with Riemann-Liouville and Caputo derivatives as well as with different types of initial and boundary conditions, local, nonlocal, involving values of solutions or their fractional integrals, delay [1,2,3,4,5,6,7]
Sensitivity of such a problem with an integral term of Fredholm type as well as of a problem containing the both terms will be considered
Summary
We consider the following fractional Integrodifferential Cauchy problem of Volterra type of order α ∈ (0, 1): t. Fractional functional systems, including Integrodifferential ones, have recently been studied by several authors. The reasons for this interest are numerous applications of fractional differential calculus in physics, chemistry, biology, economics, signal processing, image processing, aerodynamics, and so forth. We propose a new method for the study problems of type (1), namely, a theorem on diffeomorphism between Banach and Hilbert spaces obtained by the authors in paper [8]. This theorem is based on the Palais-Smale condition. Sensitivity of fractional systems of type (1) has not been studied by other authors so far
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