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Integral and Integro-Differential Equations
Published in K.T. Chau, Theory of Differential Equations in Engineering and Mechanics, 2017
Despite the similarity between the Fredholm integral equation and the Volterra integral equation, there is a major diff erence between them. In particular, iffand K in (11.267) and (11.268) are continuous, there is a unique solution for the linear nonhomogeneous Volterra integral equation of the second kind. However, for a linear nonhomogeneous Fredholm integral equation of the second kind to have a unique solution, the Fredholm alternative theorem must be satisfied.
Fredholm Integral Equation in Electrochemistry
Published in Mihai V. Putz, New Frontiers in Nanochemistry, 2020
Mirela I. Iorga, Mihai V. Putz
In particularly, Fredholm integral equation is frequently used in electrochemistry, mechanics, geophysics, electricity, magnetism, kinetic theory of gases, quantum mechanics, quantum chemistry, hereditary phenomena in biology, medicine, ecology, etc., the solutions of this equation lead to a more readily determination of processes parameters.
Biparametric identification for a free boundary of ductal carcinoma in situ
Published in Applicable Analysis, 2023
Using the operator defined by Lemma 4.1, we obtain the integral equation equivalent to (32): By (32) and the initial and final measurement and , we get Thus (40) is transformed into a Fredholm integral equation of the first kind with respect to unknown parameter where here According to hypothesis (H1) and Lemma 4.2, there is and , we have where is a convergent positive series since . By hypothesis (H1)–(H3) and Lemmas 4.3– 4.4, converges uniformly to , which can be written as Since and from Lemma 4.3 and hypothesis (H3), then , and converge uniformly for . Therefore we have and . Similarly, and converges uniformly for , so converge uniformly to , which can be represented as So the integral Equation (41) becomes Step 3. Uniqueness solution to Fredholm integral equation of the first kind.