A fast numerical algorithm based on the Taylor wavelets for solving the fractional integro‐differential equations with weakly singular kernels
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DOI: 10.1002/mma.5663
Abstract: In this paper, a fast numerical algorithm based on the Taylor wavelets is proposed for finding the numerical solutions of the fractional integro‐differential equations with weakly singular kernels. The properties of Taylor wavelets are given,… read more here.
Keywords: taylor wavelets; numerical algorithm; algorithm based; fast numerical ... See more keywords
Existence and uniqueness of solutions for nonlinear Volterra‐Fredholm integro‐differential equation of fractional order with boundary conditions
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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
Existence of solutions for some non‐Fredholm integro‐differential equations with the bi‐Laplacian
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DOI: 10.1002/mma.6721
Abstract: We prove the existence of solutions for some semilinear elliptic equations in the appropriate H4 spaces using the fixed‐point technique where the elliptic equation contains fourth‐order differential operators with and without Fredholm property, generalizing the… read more here.
Keywords: solutions non; integro differential; non fredholm; fredholm integro ... See more keywords
Approximate controllability of nonlocal impulsive neutral integro‐differential equations with finite delay
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DOI: 10.1002/mma.7753
Abstract: In this paper, we apply the resolvent operator theory and an approximating technique to derive the existence and controllability results for nonlocal impulsive neutral integro‐differential equations with finite delay in a Hilbert space. To establish… read more here.
Keywords: nonlocal impulsive; impulsive neutral; equations finite; integro differential ... See more keywords
Solvability and Stability for Neutral Stochastic Integro-differential Equations Driven by Fractional Brownian Motion with Impulses
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DOI: 10.1007/s00009-018-1253-2
Abstract: The paper is devoted to the existence, uniqueness and asymptotic behaviors of mild solution to neutral impulsive stochastic integro-differential equations driven by fractional Brownian motion with $$H\in (\frac{1}{2},1)$$H∈(12,1) by the theory of resolvent operator and… read more here.
Keywords: integro differential; fractional brownian; driven fractional; equations driven ... See more keywords
On Nonlinear Fractional Integro–Differential Equations with Positive Constant Coefficient
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DOI: 10.1007/s00009-019-1325-y
Abstract: The aim of this study is to investigate the existence and other properties of solution of nonlinear fractional integro–differential equations with constant coefficient. Also with the help of Pachpatte’s inequality, we prove the continuous dependence… read more here.
Keywords: constant coefficient; integro differential; nonlinear fractional; differential equations ... See more keywords
The Bernstein Technique for Integro-Differential Equations
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DOI: 10.1007/s00205-021-01749-x
Abstract: We extend the classical Bernstein technique to the setting of integro-differential operators. As a consequence, we provide first and one-sided second derivative estimates for solutions to fractional equations, including some convex fully nonlinear equations of… read more here.
Keywords: bernstein technique; integro differential; technique integro; differential equations ... See more keywords
A fractional spectral method with applications to some singular problems
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DOI: 10.1007/s10444-016-9511-y
Abstract: In this paper we propose and analyze fractional spectral methods for a class of integro-differential equations and fractional differential equations. The proposed methods make new use of the classical fractional polynomials, also known as Müntz… read more here.
Keywords: applications singular; integro differential; spectral method; differential equations ... See more keywords
Existence and Uniqueness of an Inverse Memory Kernel for an Integro-Differential Parabolic Equation with Free Boundary
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DOI: 10.1007/s10883-017-9372-9
Abstract: We consider an inverse problem for an integro-differential parabolic equation with free boundary. This inverse problem aims to identify the memory kernel function from a global measurement data. Based on a fixed point argument, we… read more here.
Keywords: parabolic equation; integro differential; differential parabolic; memory kernel ... See more keywords
Adomian decomposition and homotopy perturbation method for the solution of time fractional partial integro-differential equations
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DOI: 10.1007/s12190-021-01613-x
Abstract: This article deals with two different methods to solve a time fractional partial integro-differential equation. The fractional derivatives are defined here in Caputo sense. The model problem is solved using the Adomian decomposition method and… read more here.
Keywords: fractional partial; integro differential; time fractional; partial integro ... See more keywords
Controllability of neutral stochastic integro-differential evolution equations driven by a fractional Brownian motion
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DOI: 10.1007/s13370-016-0439-7
Abstract: We establish sufficient conditions for the controllability of a certain class of neutral stochastic functional integro-differential evolution equations in Hilbert spaces. The results are obtained using semigroup theory, resolvent operators and a fixed-point technique. An… read more here.
Keywords: integro; integro differential; evolution equations; fractional brownian ... See more keywords