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Solution of Fredholm integrodifferential equation for an infinite elastic plate

Alaa A. El-Bary (2004)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Many authors discussed the problem of an elastic infinite plate with a curvilinear hole, some of them considered this problem in z-plane and the others in the s-plane. They obtained an exact expression for Goursat's functions for the first and second fundamental problem. In this paper, we use the Cauchy integral method to obtain a solution to the first and second fundamental problem by using a new transformation. Some applications are investigated and also some special cases are discussed.

Solution to Fredholm integral inclusions via ( F, δ b )-contractions

Hemant Kumar Nashine, Ravi P. Agarwal, Zoran Kadelburg (2016)

Open Mathematics

We present sufficient conditions for the existence of solutions of Fredholm integral inclusion equations using new sort of contractions, named as multivalued almost F -contractions and multivalued almost F -contraction pairs under ı-distance, defined in b-metric spaces. We give its relevance to fixed point results in orbitally complete b-metric spaces. To rationalize the notions and outcome, we illustrate the appropriate examples.

Solvability of an Infinite System of Singular Integral Equations

El Borai, Mahmoud M., Abbas, Mohamed I. (2007)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 45G15, 26A33, 32A55, 46E15.Schauder's fixed point theorem is used to establish an existence result for an infinite system of singular integral equations in the form: (1) xi(t) = ai(t)+ ∫t0 (t − s)− α (s, x1(s), x2(s), …) ds, where i = 1,2,…, α ∈ (0,1) and t ∈ I = [0,T]. The result obtained is applied to show the solvability of an infinite system of differential equation of fractional orders.

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