Reachability of fractional dynamical systems using ψ-Hilfer pseudo-fractional derivative

Abstract

In this paper, we investigate the reachability of linear and nonlinear systems in the sense of the ψ-Hilfer pseudo-fractional derivative in gcalculus by means of the Mittag-Leffler functions (one and two parameters). In this sense, two numerical examples are discussed, in order to elucidate the investigated results.

Examining reachability of fractional dynamical systems with delays in control utilizing ψ-Hilfer pseudo-fractional derivative

“…By applying the g-Laplace transform method [17] on both sides of (15) and applying the well-known result of unsymmetric Fubini theorem [41], we get where L 1 (ς, λ), L 2 (ς, λ, l) and L 3 (ς, λ, l) are already defined above and…”

“…In fractional calculus and g-calculus, there is still a little unaddressed research. Using ψ-Hilfer pseudo-fractional derivative, Jose et al [17] searched for the reachability criteria of fractional mathematical systems. Panneer Selvam et al [18] explored the reachability results for fractional mathematical systems involving multiple control delays in the context of ψ-Hilfer pseudofractional derivative exploiting fixed point theory.…”

Delayed analogue of three-parameter pseudo-Mittag-Leffler functions and their applications to Hilfer pseudo-fractional time retarded differential equations

“…1 The existence and uniqueness problems of FDEs with constant delay and the stability of their solutions are crucial topics in the field of fractional differential equations. Many renowned scientists, such as Ahmed et al, 2 Moniri et al, 3 Vivek et al, 4 Mahmudov et al, [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] Khusainov et al, 23 Podlubny, 24 and Sousa et al 1,25 have made significant contributions to these problems. 1,[26][27][28][29][30][31][32] In conclusion, fractional differential equations and pseudo-analysis are fascinating areas of research with wide-ranging applications in various fields.…”

Controllability of Hilfer Fractional Semilinear Integro-Differential Equation of Order α ∊ (0, 1), β ∊ [0, 1]

“…Ma et al [17] formulated the mild solution and necessary conditions for approximate controllability of hemivariational inequalities in Sobolev-type Hilfer fractional neutral stochastic evolution systems. Sousa et al [18] explored the reachability of both linear and non-linear systems using the concept of the ψ-Hilfer pseudo-fractional derivative in g-calculus, utilizing the Mittag-Leffler functions. Johnson et al [19] studied the existence of solutions and optimal controllability of Hilfer fractional stochastic integro-differential systems with infinite delay.…”