Generalized weakly singular Gronwall-type inequalities and their applications to fractional differential equations

zbMath1483.26010MaRDI QIDQ1983199

Minh Dien Nguyen

Publication date: 10 September 2021

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Langevin equationfractional differential equationsGronwall inequality\( \psi \)-Hilfer fractional derivativeweakly singular source

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Fractional derivatives and integrals (26A33) Inequalities involving derivatives and differential and integral operators (26D10) Fractional ordinary differential equations (34A08)

Related Items (5)

Weakly singular Henry-Gronwall-Bihari type inequalities and their applications ⋮ On mild solutions of the p-Laplacian fractional Langevin equations with anti-periodic type boundary conditions ⋮ The generalized nonlocal boundary condition for fractional Langevin equation with a weakly singular source ⋮ On a multi‐point p$$ p $$‐Laplacian fractional differential equation with generalized fractional derivatives ⋮ On mild solutions of the generalized nonlinear fractional pseudo-parabolic equation with a nonlocal condition

Cites Work

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• On the \(\psi\)-Hilfer fractional derivative
• Existence and uniqueness of solutions of initial value problems for nonlinear Langevin equation involving two fractional orders
• The stability of solutions of linear differential equations
• A Gronwall inequality and the Cauchy-type problem by means of ψ-Hilfer operator
• A New Generalized Gronwall Inequality with a Double Singularity and Its Applications to Fractional Stochastic Differential Equations

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