<p>In this paper, anti-periodic boundary value problems for Caputo fractional differential equations involving the p-Laplacian operator and a singular nonlinearity of the form&#xa0;<InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <msup> <mi>t</mi> <mrow> <mo>−</mo> <mi>γ</mi> </mrow> </msup> </math></EquationSource> <EquationSource Format="TEX">$t^{-\gamma}$</EquationSource> </InlineEquation> are studied. Using tools from functional analysis together with Schaefer fixed point theorem, a global existence result for the considered problem is obtained. In order to apply the fixed point argument, we first establish the equivalence between the fractional differential problem and a corresponding Volterra integral equation. The singular term plays a crucial role throughout the analysis and requires additional estimates. An illustrative example is provided to demonstrate the applicability of the main theorem.</p>

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Anti-periodic boundary value problems for singular fractional p-Laplacian equations

  • Mahir Hasanov

摘要

In this paper, anti-periodic boundary value problems for Caputo fractional differential equations involving the p-Laplacian operator and a singular nonlinearity of the form  t γ $t^{-\gamma}$ are studied. Using tools from functional analysis together with Schaefer fixed point theorem, a global existence result for the considered problem is obtained. In order to apply the fixed point argument, we first establish the equivalence between the fractional differential problem and a corresponding Volterra integral equation. The singular term plays a crucial role throughout the analysis and requires additional estimates. An illustrative example is provided to demonstrate the applicability of the main theorem.