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<p>This paper investigates the local existence of solutions for a class of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(d\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>d</mi> </math></EquationSource> </InlineEquation>-dimensional nonlinear time-fractional diffusion equations involving the <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\psi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ψ</mi> </math></EquationSource> </InlineEquation>-Caputo fractional derivative and the <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\phi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϕ</mi> </math></EquationSource> </InlineEquation>-fractional Laplacian. By means of the generalized Laplace transform, the Fourier transform with respect to <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\phi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϕ</mi> </math></EquationSource> </InlineEquation>, and Fox <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(H\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>H</mi> </math></EquationSource> </InlineEquation>-functions, we derive the fundamental solution for the corresponding linear problem. Moreover, the local existence and uniqueness of mild solutions are rigorously established for the associated nonlinear problem.</p>

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On a class of time-fractional diffusion equations with exponential nonlinearity involving the \(\psi \)-Caputo fractional derivative and the \(\phi \)-fractional Laplacian

  • 期刊论文

  • 发表日期：

    2026年6月26日

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  • Yacine Arioua,
  • Brahim Benaissi

摘要

This paper investigates the local existence of solutions for a class of \(d\) d -dimensional nonlinear time-fractional diffusion equations involving the \(\psi \) ψ -Caputo fractional derivative and the \(\phi \) ϕ -fractional Laplacian. By means of the generalized Laplace transform, the Fourier transform with respect to \(\phi \) ϕ , and Fox \(H\) H -functions, we derive the fundamental solution for the corresponding linear problem. Moreover, the local existence and uniqueness of mild solutions are rigorously established for the associated nonlinear problem.