NON-EXISTENCE OF GLOBAL SOLUTIONS TO A SYSTEM OF FRACTIONALLY DAMPED FRACTIONAL DIFFERENTIAL PROBLEMS

Faouzi Tebessi (), Mohammed Cherif Bahi, Belgacem Rebiai, Mufda Alrawashdeh and Taha Radwan
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Faouzi Tebessi: Department of Mathematics, Echahid Cheikh Larbi Tebessi University, Tebessa, Algeria
Mohammed Cherif Bahi: Department of Mathematics, Echahid Cheikh Larbi Tebessi University, Tebessa, Algeria2Laboratory of Mathematics Informatics and Systems (LAMIS), Echahid Cheikh Larbi Tebessi University, Tebessa, Algeria
Belgacem Rebiai: Department of Mathematics, Echahid Cheikh Larbi Tebessi University, Tebessa, Algeria2Laboratory of Mathematics Informatics and Systems (LAMIS), Echahid Cheikh Larbi Tebessi University, Tebessa, Algeria
Mufda Alrawashdeh: Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia
Taha Radwan: Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia

FRACTALS (fractals), 2025, vol. 33, issue 04, 1-14

Abstract: In this paper, we consider solving a system of fractional differential equations with nonlinear source term. The nonlocal source term is a convolution of an exponential with a kernel. The solved system is able to be seen as a generalization of a number of varied systems of equations with solutions that blows up in a finite time. Under initial conditions, the nontrivial global solutions blow-up and certain assumptions are established by the weak formulation of the problem with some estimation inequalities.

Keywords: Fractional Derivatives; Fractional Differential Equations; Nonlinear Source; Global Solution; Blow-Up (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X2540095X

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