Initial value problem for fractional Volterra integro-differential equations with Caputo derivative

DOI10.3934/DCDSB.2021030zbMath1478.35226OpenAlexW3127362340WikidataQ115219195 ScholiaQ115219195MaRDI QIDQ2056212

Nguyen Huy Tuan, Yong Zhou, Huu Can Nguyen, Renhai Wang

Publication date: 1 December 2021

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2021030

zbMATH Keywords

blow-upmild solutionVolterra integro-differential equationsCaputo derivativeglobal and local existence

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Nonlinear ill-posed problems (47J06) Ultraparabolic equations, pseudoparabolic equations, etc. (35K70) Linear operators and ill-posed problems, regularization (47A52) Blow-up in context of PDEs (35B44) Semilinear parabolic equations (35K58) Fractional partial differential equations (35R11) Quasilinear parabolic equations with (p)-Laplacian (35K92) Integro-partial differential equations (35R09)

Related Items (11)

On a time fractional diffusion with nonlocal in time conditions ⋮ On the blow-up of solutions for a fractional diffusion equation with nonlinear memory and reaction terms in a bounded domain ⋮ NEW RESULTS FOR PARABOLIC EQUATION ON THE SPHERE WITH CAPUTO–FABRIZIO OPERATOR ⋮ Notes on continuity result for conformable diffusion equation on the sphere: the linear case ⋮ Forward dynamics and memory effect in a fractional order chemostat minimal model with non-monotonic growth ⋮ Well-posedness results for nonlinear fractional diffusion equation with memory quantity ⋮ GLOBAL WELL-POSEDNESS OF A CAUCHY PROBLEM FOR A NONLINEAR PARABOLIC EQUATION WITH MEMORY ⋮ The dependence on fractional orders of mild solutions to the fractional diffusion equation with memory ⋮ On fractional diffusion equation with Caputo-Fabrizio derivative and memory term ⋮ Existence of Optimal Control for a Class of Kirchhoff–Poisson System ⋮ Mild solutions to a time-fractional Cauchy problem with nonlocal nonlinearity in Besov spaces

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