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On multi-singular integral equations involving n weakly singular kernels
Filomat, 2018 We deal with some sources of Banach spaces which are closely related to an important issue in applied mathematics i.e. the problem of existence and uniqueness of the solution for the very applicable weakly singular integral equations. In the classical mode, the uniform space (C[a,b], ||.||?) is usually applied to the related discussion ...
Sales, S. M. S. Nabavi, Baghani, O.
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International Journal of Differential Equations, 2018 An analytical-approximate method is proposed for a type of nonlinear Volterra partial integro-differential equations with a weakly singular kernel. This method is based on the fractional differential transform method (FDTM).
Rezvan Ghoochani-Shirvan +2 more
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analysis of Product Integration Methods for a Class of Singular Volterra Integral Equations
Trends in Computational and Applied Mathematics, 2000 The construction and analysis of high order numerical methods for Volterra integral equations with a certain weakly singular kernel have been investigated in [6], under the assumption the the solution is sufficiently smooth.
T. Diogo, P. Lima, N.B. Franco
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Journal of Inequalities and Applications, 2016 Some new inequalities with weakly singular integral kernel are developed, which generalize some known inequalities and can be used in the qualitative and quantitative analysis of the solutions to certain fractional differential equations.
Run Xu, Fanwei Meng
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Collocation Solutions of a Weakly Singular Volterra Integral Equation
Trends in Computational and Applied Mathematics, 2007 The discrete superconvergence properties of spline collocation solutions for a certain Volterra integral equation with weakly singular kernel are analyzed.
T. Diogo, P. Lima
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Advanced Modeling and Simulation in Engineering Sciences, 2021 In this study, we applied an advanced barycentric Lagrange interpolation formula to find the interpolate solutions of weakly singular Fredholm integral equations of the second kind.
E. S. Shoukralla +2 more
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Comput. Math. Methods, 2021 Fractional integro-differential equation (FIDE) with weakly singular kernel is an important topic in mathematics and engineering dealing with mathematical modeling and simulation of numerous systems and processes.
Jyotirmoy Mouley, B. N. Mandal
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On operators induced by weakly 2-singular kernels [PDF]
Czechoslovak Mathematical Journal, 1995 It is shown that a kernel \(K(x,y)= L(x,y)/| x-y|^{1/2}\) for \(x\neq y\) in \([0,1]\) defines a \((q,2)\)-summing operator on \(L_\infty(0,1)\) for any \(q>2\) provided that \(\sup_x| L(x,\cdot)|\in L_{2,1}(0,1)\).
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A Hybrid Collocation Method for Volterra Integral Equations with Weakly Singular Kernels [PDF]
SIAM Journal on Numerical Analysis, 2003 This paper presents a new hybrid collocation method for solving certain second kind Volterra integral equations with singular kernels. The solution of the equation has a singularity, caused by the singularity in the kernel, and this presents particular challenges for numerical schemes.
Cao, Y. Z., Herdman, Terry L., Xu, Y. H.
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RBFs for Integral Equations with a Weakly Singular Kernel [PDF]
American Journal of Applied Mathematics, 2015 In this paper a numerical method, based on collocation method and radial basis functions (RBF) is proposed for solving integral equations with a weakly singular kernel. Integrals appeared in the procedure of the solution are approximated by adaptive Lobatto quadrature rule.
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