Results 11 to 20 of about 22,371 (264)
Solving special systems of integral equations by using Sumudu transform with a semi-analytical method [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2023 In this paper, specific forms of non-linear systems of integral equations have been solved using the Sumudu transform and the Adomian decomposition method.
Waleed Al-Hayani
doaj +1 more source
Existence Theorem for Integral and Functional Integral Equations with Discontinuous Kernels
Abstract and Applied Analysis, 2012 Existence of extremal solutions of nonlinear discontinuous integral equations of Volterra type is proved. This result is extended herein to functional Volterra integral equations (FVIEs) and to a system of discontinuous VIEs as well.
Ezzat R. Hassan
doaj +1 more source
New Retarded Integral Inequalities with Applications
Journal of Inequalities and Applications, 2008 Some new nonlinear integral inequalities of Gronwall type for retarded functions are established, which extend the results Lipovan (2003) and Pachpatte (2004).
S. K. Sen, Young-Ho Kim, Ravi P. Agarwal
doaj +2 more sources
Lyapunov Functionals in Integral Equations
Axioms, 2023 Lyapunov functions/functionals have found their footing in Volterra integro-differential equations. This is not the case for integral equations, and it is therefore further explored in this paper. In this manuscript, we utilize Lyapunov functionals combined with Laplace transform to qualitatively analyze the solutions of the integral equation In ...
Youssef N. Raffoul, Joseph Raffoul
openaire +2 more sources
Mathematics, 2023 Cauchy problems are considered for families of, generally speaking, non-Volterra functional differential equations of the second order. For each family considered, in terms of the parameters of this family, necessary and sufficient conditions for the ...
Eugene Bravyi
doaj +1 more source
Monotonic solutions of functional integral and differential equations of fractional order
Electronic Journal of Qualitative Theory of Differential Equations, 2009 The existence of positive monotonic solutions, in the class of continuous functions, for some nonlinear quadratic integral equations have been studied by J. Banas. Here we are concerned with a singular quadratic functional integral equations.
Ahmed El-Sayed, H. H. G. Hashem
doaj +1 more source
Discrete integrable equations and special functions [PDF]
Ufimskii Matematicheskii Zhurnal, 2017 Summary: A generic scheme based on the matrix Riemann-Hilbert problem theory is proposed for constructing classical special functions satisfying difference equations. These functions comprise gamma- and zeta functions, as well as orthogonal polynomials with corresponding recurrence relations.
openaire +1 more source
On global attractivity of solutions of a functional-integral equation
Electronic Journal of Qualitative Theory of Differential Equations, 2007 We prove an existence theorem for a quadratic functional-integral equation of mixed type. The functional-integral equation studied below contains as special cases numerous integral equations encountered in nonlinear analysis.
Mohamed Darwish
doaj +1 more source
An Integral Equation Involving Legendre Functions [PDF]
Journal of the Society for Industrial and Applied Mathematics, 1964 Rodrigues’s formula can be applied also to (1.1) and (1.3) but here the situation is slightly more involved in that the integrals with respect to σ^2 are of fractional order and their inversion requires the knowledge of differentiation and integration of fractional order.
openaire +2 more sources
Some Integral Equations Involving Hypergeometric Functions [PDF]
Proceedings of the Edinburgh Mathematical Society, 1967 SummaryAn integral equation of the first kind, with kernel involving a hypergeometric function, is discussed. Conditions sufficient for uniqueness of solutions are given, then conditions necessary for existence of solutions. Conditions sufficient for existence of solutions, only a little stricter than the necessary conditions, are given; and with them ...
openaire +1 more source