On the Recovery of a Conformable Time-Dependent Inverse Coefficient Problem for Diffusion Equation of Periodic Constraints Type and Integral Over-Posed Data

Abstract

In the utilized analysis, we consider the inverse coefficient problem of recovering the time-dependent diffusion coefficient along the solution of the conformable time-diffusion equation subject to periodic boundary conditions and an integral over-posed data. Along with this, the conformable time derivative with order <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mn>0</a:mn> <a:mo>&lt;</a:mo> <a:mi>η</a:mi> <a:mo>≤</a:mo> <a:mn>1</a:mn> </a:math> is defined in the sense of a limit operator. The formal solution set for the considered inverse coefficient conformable problem is acquired via utilizing the Fourier expansion method. Under some conditions on the data and applicability of the Banach theorem, we insured the existence and uniqueness of the regular solution. Continuous dependence of the solutions set <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"> <c:mfenced open="{" close="}" separators="|"> <c:mrow> <c:mi>q</c:mi> <c:mfenced open="(" close=")" separators="|"> <c:mrow> <c:mi>t</c:mi> </c:mrow> </c:mfenced> <c:mo>,</c:mo> <c:mi>u</c:mi> <c:mfenced open="(" close=")" separators="|"> <c:mrow> <c:mi>x</c:mi> <c:mo>,</c:mo> <c:mi>t</c:mi> </c:mrow> </c:mfenced> </c:mrow> </c:mfenced> </c:math> in the given data is shown. Couples of illustrative examples in the form of data results and computational figures are also utilized. Future remarks, highlights, and work results are epitomized in the penultimate part. Finally, some latest used and focused references are given.

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