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<p>In this paper, we consider the sum of linear fractional-power operators acting in a Banach space and satisfying weak positivity. We establish the correct solvability of the problem for the corresponding fractional-operator equation and we give the representation of the solution through the inverse operator with an exact estimate of its norm. The results are applied to problems without initial conditions for an equation with singular coefficients. We consider examples of such equations.</p>

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CORRECT SOLVABILITY OF PROBLEMS FOR FRACTIONAL-POWER OPERATOR EQUATIONS

  • 期刊论文

  • 发表日期：

    2025年7月1日

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  • S. D. Baboshin

摘要

In this paper, we consider the sum of linear fractional-power operators acting in a Banach space and satisfying weak positivity. We establish the correct solvability of the problem for the corresponding fractional-operator equation and we give the representation of the solution through the inverse operator with an exact estimate of its norm. The results are applied to problems without initial conditions for an equation with singular coefficients. We consider examples of such equations.