Existence and uniqueness of solutions for nonlinear Volterra‐Fredholm integro‐differential equation of fractional order with boundary conditions
Sign Up to like & getrecommendations! Published in 2019 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.5845
Abstract: In this paper, we established some results concerning the existence and uniqueness of a nonlinear Volterra‐Fredholm integro‐differential equation of Caputo fractional order subject to the boundary value conditions. These new results are obtained by applying… read more here.
Keywords: existence uniqueness; volterra fredholm; integro differential; differential equation ... See more keywords
Analysis of collocation methods for nonlinear Volterra integral equations of the third kind
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DOI: 10.1007/s10092-019-0304-9
Abstract: We study the approximation of solutions of a class of nonlinear Volterra integral equations (VIEs) of the third kind by using collocation in certain piecewise polynomial spaces. If the underlying Volterra integral operator is not… read more here.
Keywords: integral equations; volterra integral; third kind; collocation ... See more keywords
A Fractional Spectral Collocation for Solving Second Kind Nonlinear Volterra Integral Equations with Weakly Singular Kernels
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DOI: 10.1007/s10915-019-00987-2
Abstract: The classical integer-order Jacobi spectral methods for solving second kind nonlinear Volterra integral equations with weakly singular kernels may cause a low-order accuracy in numerically approximating the exact solution. To overcome the shortcomings, we in… read more here.
Keywords: collocation; integral equations; volterra integral; fractional spectral ... See more keywords
New Stability Criteria for Nonlinear Volterra Integro-Differential Equations
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DOI: 10.1007/s40306-017-0243-y
Abstract: Using a novel approach, we present some new explicit criteria for the uniform asymptotic stability and the exponential stability of nonlinear Volterra integro-differential equations. Some examples are given to illustrate the obtained results. read more here.
Keywords: integro differential; differential equations; stability; volterra integro ... See more keywords
A Novel Method for Solving Nonlinear Volterra Integro-Differential Equation Systems
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DOI: 10.1155/2018/3569139
Abstract: An efficient iteration method is introduced and used for solving a type of system of nonlinear Volterra integro-differential equations. The scheme is based on a combination of the spectral collocation technique and the parametric iteration… read more here.
Keywords: novel method; integro differential; method; volterra integro ... See more keywords
Ulam-Hyers stability for a nonlinear Volterra integro-differential equation
Sign Up to like & getrecommendations! Published in 2019 at "Hacettepe Journal of Mathematics and Statistics"
DOI: 10.15672/hujms.483606
Abstract: In this work, the Ulam-Hyers stability and the Ulam-Hyers-Rassias stability for the nonlinear Volterra integro-differential equations are established by employing the method of successive approximation. Some simple examples are given to illustrate the main results.… read more here.
Keywords: stability nonlinear; volterra integro; hyers stability; stability ... See more keywords
Nonlinear Volterra Integrodifferential Equations from above on Unbounded Time Scales
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DOI: 10.3390/math11071760
Abstract: The paper is devoted to studying the existence, uniqueness and certain growth rates of solutions with certain implicit Volterra-type integrodifferential equations on unbounded from above time scales. We consider the case where the integrand is… read more here.
Keywords: equations unbounded; nonlinear volterra; integrodifferential equations; time scales ... See more keywords
A Numerical Method for Weakly Singular Nonlinear Volterra Integral Equations of the Second Kind
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DOI: 10.3390/sym12111862
Abstract: This paper presents a numerical iterative method for the approximate solutions of nonlinear Volterra integral equations of the second kind, with weakly singular kernels. We derive conditions so that a unique solution of such equations… read more here.
Keywords: second kind; integral equations; method; equations second ... See more keywords
Symmetric Spectral Collocation Method for a Kind of Nonlinear Volterra Integral Equation
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DOI: 10.3390/sym14061091
Abstract: In this paper, we develop an efficient spectral method for numerically solving the nonlinear Volterra integral equation with weak singularity and delays. Based on the symmetric collocation points, the spectral method is illustrated, and the… read more here.
Keywords: integral equation; nonlinear volterra; collocation; method ... See more keywords