A Gronwall inequality via the generalized proportional fractional derivative with applications
From MaRDI portal
Publication:2067825
DOI10.1186/s13660-019-2052-4zbMath1499.26092OpenAlexW2944787851WikidataQ128073683 ScholiaQ128073683MaRDI QIDQ2067825
Thabet Abdeljawad, Fahd Jarad, Weerawat Sudsutad, Jehad O. Alzabut
Publication date: 19 January 2022
Published in: Journal of Inequalities and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1186/s13660-019-2052-4
uniqueness of solutionbound for the solutiondelay proportional fractional systemproportional Gronwall inequality
Fractional derivatives and integrals (26A33) Mittag-Leffler functions and generalizations (33E12) Inequalities for sums, series and integrals (26D15)
Related Items
Certain new weighted estimates proposing generalized proportional fractional operator in another sense, Nonlocal boundary value problems for integro-differential Langevin equation via the generalized Caputo proportional fractional derivative, Ulam's type stability analysis of fractional difference equation with impulse: Gronwall inequality approach, On the oscillation of differential equations in frame of generalized proportional fractional derivatives, New generalizations for Gronwall type inequalities involving a \(\psi\)-fractional operator and their applications, Some new fractional inequalities involving convex functions and generalized fractional integral operator, Existence results of nonlinear generalized proportional fractional differential inclusions via the diagonalization technique, On some Hermite-Hadamard type inequalities for \(tgs\)-convex functions via generalized fractional integrals, Analysis and applications of the proportional Caputo derivative, Generalized proportional fractional integral functional bounds in Minkowski's inequalities, Grüss-type integrals inequalities via generalized proportional fractional operators, Generalized proportional fractional integral inequalities for convex functions, NEW GENERALIZATION INVOLVING CONVEX FUNCTIONS VIA ℏ-DISCRETE 𝒜ℬ-FRACTIONAL SUMS AND THEIR APPLICATIONS IN FRACTIONAL DIFFERENCE EQUATIONS, A Gronwall inequality and its applications to the Cauchy-type problem under \(\psi\)-Hilfer proportional fractional operators, Some existence and uniqueness results for a class of proportional Liouville-Caputo fractional stochastic differential equations, A class of fractional differential equations via power non-local and non-singular kernels: existence, uniqueness and numerical approximations, Unnamed Item, Some new bounds analogous to generalized proportional fractional integral operator with respect to another function, Analysis and numerical solution of the generalized proportional fractional Cauchy problem, Novel comparison of numerical and analytical methods for fractional Burger-Fisher equation, Some fractional proportional integral inequalities, Ulam stability of Caputo \(q\)-fractional delay difference equation: \(q\)-fractional Gronwall inequality approach, Certain Grüss-type inequalities via tempered fractional integrals concerning another function, New estimates considering the generalized proportional Hadamard fractional integral operators, Extensions of Gronwall-Bellman type integral inequalities with two independent variables, NEW ESTIMATES OF INTEGRAL INEQUALITIES VIA GENERALIZED PROPORTIONAL FRACTIONAL INTEGRAL OPERATOR WITH RESPECT TO ANOTHER FUNCTION, Certain inequalities via generalized proportional Hadamard fractional integral operators, The Minkowski inequalities via generalized proportional fractional integral operators, A new approach to interval-valued inequalities
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A generalized \(q\)-fractional Gronwall inequality and its applications to nonlinear delay \(q\)-fractional difference systems
- On conformable fractional calculus
- Lyapunov-type inequalities for mixed non-linear forced differential equations within conformable derivatives
- A generalized Gronwall inequality and its application to a fractional differential equation
- Gronwall's inequality for functions of two independent variables
- Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
- Recent applications of fractional calculus to science and engineering
- Fractional operators with exponential kernels and a Lyapunov type inequality
- A generalized Lyapunov-type inequality in the frame of conformable derivatives
- A note on Gronwall's inequality on time scales
- On a class of ordinary differential equations in the frame of Atangana-Baleanu fractional derivative
- A new definition of fractional derivative
- Nonlinear Gronwall-Bellman type inequalities and their applications
- A generalized discrete fractional Gronwall inequality and its application on the uniqueness of solutions for nonlinear delay fractional difference system
- A discrete fractional Gronwall inequality
- Inequalities
- A generalized Gronwall inequality and its application to fractional neutral evolution inclusions