Existence and uniqueness of periodic solutions for some nonlinear fractional pantograph differential equations with $$\psi $$-Caputo derivative

Abstract

The aim of this paper is to study the existence and uniqueness of periodic solutions for a certain type of nonlinear fractional pantograph differential equation with a $$\psi $$ ψ -Caputo derivative. The proofs are based on the coincidence degree theory of Mawhin. To show the efficiency of the results, some illustrative examples are included.

Controllability of fractional dynamical systems with ψ-Caputo fractional derivative

“…Aydi et al examined the existence and uniqueness of positive solutions for a fractional thermostat model for both cases of concave and convex source terms by utilizing ψ-Caputo fractional derivative in [9]. For reference, [10][11][12][13][14][15][16] these are certain articles on differential equations that heavily rely on the ψ-Caputo fractional derivative.…”

On Nonlinear Periodic Problems with Caputo's Exponential Fractional Derivative

“…In [16], Bouriah et al considered the following nonlinear pantograph fractional equation with ψ-Caputo fractional derivative: c D α;ψ 0 + φ(ϑ) = Ψ(ϑ, φ(ϑ), φ(εϑ)), ϑ ∈ Ξ := [0, Θ], φ(0) = φ(Θ), where c D α;ψ 0 + denotes the ψ-Caputo fractional derivative of order 0 < α < 1, ε ∈ (0, 1), and Ψ : Ξ×R×R → R is a continuous function.…”

“…Finally, two examples are provided in the last section to demonstrate the applicability of our results. Our ndings are mostly based on papers [13,14,16,19], where we employed the coincidence degree theory.…”

SOLVABILITY AND ULAM-STABILITY FOR NONLINEAR DIFFERENTIAL PROBLEM WITH Phi-HILFER APPROACH

“…Indeed, the fractional differential equations describe many more phenomena than ordinary differential equations. Therefore, partial differential equations appear in many engineering and technological disciplines that include several sciences, see for example [1][2][3][4][5][6][7][8][9][10][11].…”

“…ENS of Mostaganem, Department of Exact Sciences, 27000 Mostaganem, Algeria. E-mail: beddani2004@yahoo.fr 2. Laboratory of Complex Systems of the Higher School of Electrical and Energy Engineering of Oran, 31000 Oran, Algeria.…”