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<p>This paper studies the existence of global solutions to a nonlinear fractional diffusion equation involving a <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\psi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ψ</mi> </math></EquationSource> </InlineEquation>-Caputo derivative. A fundamental solution to the linear case is derived by employing the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\psi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ψ</mi> </math></EquationSource> </InlineEquation>-Laplace transform and Fox <i>H</i>-functions. A decay estimate for the solution in Lebesgue spaces is then established. Finally, the existence, uniqueness, and well-posedness of mild global solutions to the nonlinear fractional diffusion equation are demonstrated under small initial data and modified norms.</p>

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THE FUNDAMENTAL AND GLOBAL EXISTENCE OF SOLUTIONS TO A GENERALIZED NONLINEAR FRACTIONAL DIFFUSION EQUATION WITH GRADIENT NONLINEARITY

  • 期刊论文

  • 发表日期：

    2025年11月25日

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  • Brahim Benaissi,
  • Yacine Arioua

摘要

This paper studies the existence of global solutions to a nonlinear fractional diffusion equation involving a \(\psi \) ψ -Caputo derivative. A fundamental solution to the linear case is derived by employing the \(\psi \) ψ -Laplace transform and Fox H-functions. A decay estimate for the solution in Lebesgue spaces is then established. Finally, the existence, uniqueness, and well-posedness of mild global solutions to the nonlinear fractional diffusion equation are demonstrated under small initial data and modified norms.