June 25, 2025 Journal article Open Access

GEZAGN BEKELA AYANA

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    <subfield code="a">SOLVING CAPUTO TYPE ATANGANA-BALEANU FRACTIONAL DERIVATIVE USING FIXED POINT RESULTS IN EXTENDED b-METRIC SPACES</subfield>
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    <subfield code="a">&lt;p&gt;&lt;em&gt;The fixed-point theory is an important tool in the study of nonlinear functional analysis, and it is widely applicable in pure and applied mathematics. For this reason, the current study is aimed at integrating fixed point yields extended b-metric spaces to solving Caputo type Atangana-Baleanu fractional derivative. Firstly, we conceptualize the idea extended b-metric spaces for fixed points solving Atangana-Baleanu fractional derivative. Secondly, we review extensive existing body of knowledge from seminars, proceedings, scientific article and books available online in published form. Thirdly, we prove some theorems that are not published by other researchers in the field. Moreover, we provide detail analysis of the application Extended b-metric spaces are produced by the fixed point for solving Caputo type Atangana-Baleanu fractional derivative. Finally, we provide an illustrative example in support of the study in this thesis. &lt;/em&gt;&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Keywords: &lt;/strong&gt;&lt;em&gt;Fixed point result, Banach contraction principle, Fractional calculus, Atangana-Baleanu derivative, Cyclic operator&lt;/em&gt;&lt;/p&gt;</subfield>
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