Sufficient Conditions for the Non-Existence of Global Solutions to Fractional Systems with Lower-Order Hadamard-Type Fractional Derivatives

Saeed M. Ali () and Mohammed D. Kassim
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Saeed M. Ali: Department of Basic Engineering Sciences, College of Engineering, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam 34151, Saudi Arabia
Mohammed D. Kassim: Department of Basic Engineering Sciences, College of Engineering, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam 34151, Saudi Arabia

Mathematics, 2025, vol. 13, issue 7, 1-16

Abstract: This study investigates the absence of global solutions for a system of fractional differential equations. The system features a nonlinear source term with nonlocal temporal behavior and involves two Hadamard fractional derivatives (HFDs) of varying orders. Compared to previous studies, this system offers greater generality. To establish our conclusions, we employ properties of fractional derivatives, the method of test function, and integral inequality techniques. Finally, illustrative examples showcase our findings.

Keywords: method of test function; global solution; fractional differential equation; Hadamard fractional derivative; non-existence; fractional system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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