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Chaos control and sensitivity analysis of climate change under green gases and carbon omission utilizing caputo fractional operator. [PDF]

Sci Rep
Ahmad A, Khan MS, Ozsahin DU, Ahmad H, Munir A, Radwan T.   +5 more
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Transmission dynamics and stability analysis of fractional HIV and AIDS epidemic model with antiretroviral therapy. [PDF]

Sci Rep
Huang L, Anjam YN, Ali A, Rehman B, Tahir MA.   +4 more
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Attributes of residual neural networks for modeling fractional differential equations. [PDF]

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Agarwal S, Mishra LN.
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NONLINEAR VOLTERRA INTEGRAL EQUATIONS WITH CONVOLUTION KERNELS

Bulletin of the London Mathematical Society, 2003
Some new results concerning the existence and uniqueness of nontrivial solutions to the title equations are presented.
Mydlarczyk, W., Okrasiński, W.
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APPROXIMATE SOLUTIONS OF NONLINEAR VOLTERRA INTEGRAL EQUATION SYSTEMS

International Journal of Modern Physics B, 2010
The purpose of this study is to implement a new approximate method for solving system of nonlinear Volterra integral equations. The technique is based on, first, differentiating both sides of integral equations n times and then substituting the Taylor series the unknown functions in the resulting equation and later, transforming to a matrix equation ...
Yalçinbaş, Salih, Erdem, Kübra
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Nonlinear Volterra Integral Equations and the Apéry Identities

Bulletin of the London Mathematical Society, 1992
The authors study necessary and sufficient conditions for the existence of nontrivial solutions of the Volterra integral equation \(u(x)=\int_ 0^ x k(x-s) g(u(s))ds\). Using the identity \[ \begin{multlined} \int_ a^ x f(s)h(s)ds= \int_ a^ \lambda f(s)\varphi(s)ds+ \int_ a^ \lambda [f(\lambda-f(s)][\varphi(s)-h(s)]ds+\\ +\int_ \lambda^ x [f(s)- f ...
Bushell, P. J., Okrasiński, W.
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VOLTERRA INTEGRAL EQUATIONS AND NONLINEAR SEMIGROUPS

Nonlinear Analysis: Theory, Methods & Applications, 1977
Publisher Summary This chapter discusses Volterra integral equations and nonlinear semigroups. It presents the nonlinear Volterra integral equation x ( t ) = y ( t ) + ∫ g ( t − s , x ( s )) ds , t ≥ 0, where H is a Hilbert space, y : [0, ∞) → H is given, g : [0, ∞) × H → satisfies a Lipschitz condition in its second place, and x :
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Nontrivial Solutions to Nonlinear Volterra Integral Equations

SIAM Journal on Mathematical Analysis, 1991
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Approximate solutions of nonlinear two‐dimensional Volterra integral equations

Mathematical Methods in the Applied Sciences, 2021
The present work is concerned with examining the Optimal Homotopy Asymptotic Method (OHAM) for linear and nonlinear two‐dimensional Volterra integral equations (2D‐VIEs). The result obtained by the suggested method for linear 2D‐VIEs is compared with the differential transform method, Bernstein polynomial method, and piecewise block‐plus method and ...
Sumbal Ahsan, Rashid Nawaz, Muhammad Akbar, Kottakkaran Sooppy Nisar, Dumitru Baleanu   +4 more
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Nonlinear volterra integral equations of the first kind

Nonlinear Analysis: Theory, Methods & Applications, 1995
Consider the weakly singular Volterra systems of the first kind \[ \int_0^t {k \bigl( t,s,x(s) \bigr) \over (t - s)^\alpha} ds = f(t), \qquad t \in J = [0,a], \tag{*} \] where \(\alpha \in [0,1)\), \(k : \Delta \times \mathbb{R}^n \to \mathbb{R}^n\) with \(\Delta = \{(s,t) \in J^2 : s \leq t\}\) and \(f : J \to \mathbb{R}^n\) are given.
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