This manuscript is devoted to investigate the existence, uniqueness and stability of pantograph equations with Hilfer generalized proportional fractional derivative. The concerned results are obtained using standard theorems.

In this paper, the Kharrat–Toma transforms of Prabhakar integral, a Hilfer–Prabhakar (HP) fractional derivative, and regularized version HP derivative are derived. Moreover, we also compute solution some Cauchy problems diffusion equations modeled with via transform. The solutions computed in form generalized Mittag–Leffler function.

In this paper, we initially derive the equivalent fractional integral equation to $$\Psi $$ -Hilfer hybrid differential equations and through it, prove existence of a solution in weighted space. The paper’s primary objective is obtain estimates on derivative utilize it inequalities involving derivative. With assistance these inequalities, determine extremal solutions comparison theorems.

The fractional diffusion equation that is constructed replacing the time derivative with a fractional derivative, (0)D(alpha)(t) f = C(alpha) theta(2) f/theta x(2), where (0)D(alpha)(t) is the Riemann-Liouville derivative operator, is characterized by a probability density that decays with time as t(alpha -1) (alpha < 1) and an initial condition that diverges as t -->0 [R. Hilfer, J. Phys. Chem...

In this paper, we discuss the existence of solutions for hybrid stochastic differential equations (HSDEs) with $\psi$-Hilfer fractional derivative. The main tool used in our study is associated technique fixed point theorems due to Dhage.

We apply the Radu–Miheţ method derived from an alternative fixed-point theorem with a class of matrix-valued fuzzy controllers to approximate fractional Volterra integro-differential equation ψ-Hilfer derivative in k-normed spaces obtain approximation for this type equation.

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