OSCILLATORY BEHAVIOR OF Ψ-HILFER GENERALIZED PROPORTIONAL FRACTIONAL DIFFERENTIAL EQUATIONS WITH MIXED NONLINEARITIES

James, Viji; Jehad, Alzabut; Muthulakshmi, Velu; Abdullah, Ozbekler

doi:10.22034/cmde.2026.66532.3118

OSCILLATORY BEHAVIOR OF Ψ-HILFER GENERALIZED PROPORTIONAL FRACTIONAL DIFFERENTIAL EQUATIONS WITH MIXED NONLINEARITIES

Articles in Press

Document Type : Research Paper

Authors

¹ Department of Mathematics, Periyar University, Salem-636 011, Tamilnadu, India.

² 1. Department of Industrial Engineering, Ostim Technical University, Ankara 06374, Türkiye.\\ 2. Department of Mathematics and Sciences, Prince Sultan University, 11586 Riyadh, Saudi Arabia.

³ Ankara University, Faculty of Science, Department of Computer Science, Ankara, 06100, Türkiye.

10.22034/cmde.2026.66532.3118

Abstract

This paper deals with the forced oscillation of FDEs (Fractional Differential Equations) with mixed
nonlinearities via Ψ-Hilfer GPFD (Generalized Proportional Fractional Derivative). Volterra integral
equation and Young’s inequality are used to specify the appropriate conditions for each solution to
oscillate. The effects of this study enhance and generalize earlier results in the literature. Examples
are presented to illustrate the practicality of the outcomes.

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Main Subjects