weakly singular integral equation
On a weakly singular quadratic integral equations of Volterra type in Banach algebras
... Quadratic integral equations with nonsingular kernels are associated with epidemic mod- els ...quadratic integral equations with singular kernels have received a lot of attention because of their ...
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A Compact Scheme for a Partial Integro-Differential Equation with Weakly Singular Kernel
... This study is presented in the following sections: in Section 1, the product trapezoidal method and a fourth- order compact finite difference scheme for discretization of spatial derivatives are introduced. Results of ...
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On a singular integral equation with log kernel and its application
... a singular integral equation ...of singular integral equation method to solve the ...The singular integral equations arising in [2] consist of Cauchy kernel and a ...
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Jacobi spectral solution for weakly singular integral algebraic equations of index 1
... Finally, the above estimates together with equation (.) lead to Theorem . It is noted in [] that the function transformation generally makes the resulting equa- tions and approximations more complicated. As ...
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Numerical Methods for a Class of Hybrid Weakly Singular Integro Differential Equations
... determinate equation is a scalar weakly sin- gular integro-differential equation of the first ...new equation comprising additional derivative terms and integro-differential terms with smooth ...
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Some New Nonlinear Weakly Singular Integral Inequalities of Wendroff Type with Applications
... 8 H. Sano and N. Kunimatsu, “Modified Gronwall’s inequality and its application to stabilization problem for semilinear parabolic systems,” Systems & Control Letters, vol. 22, no. 2, pp. 145–156, 1994. 9 H. Ye, J. ...
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Bounds on some new weakly singular Wendroff type integral inequalities and applications
... to weakly singular integral inequalities in two variables and their applications to the partial differential equation with singular ...new weakly singular integral ...
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Generalized nonlinear weakly singular retarded integral inequalities with maxima and their applications
... nonlinear weakly singular retarded Wendroff-type integral inequality with maxima of an unknown function of two ...some singular integral equation with maxima may be ...
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Numerical Experiments on Eigenvalues of Weakly Singular Integral Equations Using Product Simpson's Rule
... the integral equation eigenvalue problem λf(x) = R −1 1 k(|x − y|)f (y)dy where k(t) = ln |t| or k(t) = t −α , 0 < α < 1, λ, f and are unknowns which we wish to ...the integral above is ...
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Some Nonlinear Weakly Singular Integral Inequalities with Two Variables and Applications
... nonlinear weakly singular integral inequalities in two variables which generalize some known results are ...equations, integral equations, and evolution ...
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On some new weakly singular Volterra integral inequalities with maxima and their applications
... with singular kernel to prove global existence and exponential decay results for a parabolic differential ...linear singular integral inequalities of Henry ...
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Analysis of Abel-type nonlinear integral equations with weakly singular kernels
... have to introduce novel techniques and results to overcome the difficult from the weakly singular kernels and nonlinear terms h and g. For example, the first important step is how to construct a suitable order ...
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Some new weakly singular integral inequalities and their applications to fractional differential equations
... Theorem . Let u(t), a(t), b(t), c(t), d(t), f (t) ∈ C[, ∞), p, m, q, α , β , γ be the same as in Theorem .. Then, for any K > , every solution of equation (.) has the bounds and the same modality as ...
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Some new weakly singular integral inequalities with discontinuous functions for two variables and their applications
... and used it to study the dependence of the solution and the initial condition to a certain fractional differential equation. All such inequalities are studied by an iteration argument, and the estimation formulas ...
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Kress smoothing transformation for weakly singular Fredholm integral equation of second kind
... Fredholm integral equation in domains with ...this integral equation has a singularity at the corner ...considers integral equations of the second kind in the slightly unconventional ...
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The Combined Reproducing Kernel Method and Taylor Series for Handling Fractional Differential Equations
... solve singular or nonsingular integral equations in the reproducing kernel Hilbert space which was pre- sented by Zaremba in ...gular integral equations with cosecant kernel [25], Fredholm ...
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A computational method for solving weakly singular Fredholm integral equation in reproducing kernel spaces
... integro-differential equation with weakly sin- gular ...Fredholm integral equations with weakly singular kernel ...Fredholm integral equa- tion of the second kind with Cauchy ...
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Discrete collocation method for Volterra type weakly singular integral equations with logarithmic kernels
... Laplace equation in two dimensions in terms of a single-layer logarithmic potential [24], solution of the reduced wave equation in two di- mensions using an integral equation with a kernel, ...
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Estimation of unknown function of nonlinear weakly singular integral inequalities of Gronwall–Bellman–Pachpatte type
... The integral inequality provides a useful tool for investigating the existence, uniqueness, boundedness and other qualitative properties of the solutions of differential equations and integral equations and ...
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Some new nonlinear integral inequalities with weakly singular kernel and their applications to FDEs
... nonlinear integral inequalities with weakly singular kernel which can be used as tools in deriving boundedness of the solutions of certain fractional differential equations and integral ...
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