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Journal of Environmental Accounting and Management 14(1) (2026) 35--45 | DOI:10.5890/JEAM.2026.03.004

Mohd Khalid$^{1,2}$, Ali Akg\"ul$^{3, 4, 5,6,7\dagger}$, Nourhane Attia$^{8,9}$, Evren Hincal$^{10}$

$^{1}$ Department of Mathematics, Lords Institute of Engineering and Technology (Autonomous), Hyderabad, India

$^2$ Department of Mathematics, Maulana Azad National Urdu University Gachibowli, Hyderabad-500032, India

$^{3}$ Department of Electronics and Communication Engineering, Saveetha School of Engineering, SIMATS, Chennai, Tamilnadu, India

$^{4}$ Siirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt, Turkey

$^{5}$ Department of Computer Engineering, Biruni University, 34010 Topkapı, Istanbul, Turkey

$^{6}$ Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulevard, PC: 99138, Nicosia /Mersin 10 – Turkey

$^7$ Applied Science Research Center, Applied Science Private University, Amman, 11937, Jordan

$^{8}$ Near East University, Department of Mathematics, Mersin 10, TRNC, Turkey

$^9$ Research Center of Applied Mathematics, Khazar University, Baku, Azerbaijan

$^{10}$ Art and Science Faculty, Department of Mathematics, Near East Boulevard, PC: 99138, Nicosia/Mersin 10, Turkey

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Abstract

In this paper, we address problems that involve the constant proportional Atangana-Baleanu-Caputo (CPABC) and constant proportional Caputo-Fabrizio (CPCF) derivatives. These derivatives introduce new challenges and opportunities in fractional calculus. Our approach is different from traditional methods like the Laplace transform; instead, we use the Shehu and Formable integral transforms to solve these problems. By using these methods, we find solutions that help us understand how systems behave with CPCF and CPABC derivatives.

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