731 citations · 12.8k across the 413 of their papers we have counts for
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Existence Results for a Multipoint Fractional Boundary Value Problem in the Fractional Derivative Banach Space
Djalal Boucenna, Amar Chidouh, Delfim F. M. Torres
We study a class of nonlinear implicit fractional differential equations subject to nonlocal boundary conditions expressed in terms of nonlinear integro-differential equations. Usi…
A Non-Newtonian Noether's Symmetry Theorem
Delfim F. M. Torres
The universal principle obtained by Emmy Noether in 1918, asserts that the invariance of a variational problem with respect to a one-parameter family of symmetry transformations im…
On a Non-Newtonian Calculus of Variations
Delfim F. M. Torres
The calculus of variations is a field of mathematical analysis born in 1687 with Newton's problem of minimal resistance, which is concerned with the maxima or minima of integral fu…
Cauchy's formula on nonempty closed sets and a new notion of Riemann--Liouville fractional integral on time scales
Delfim F. M. Torres
We prove Cauchy's formula for repeated integration on time scales. The obtained relation gives rise to new notions of fractional integration and differentiation on arbitrary nonemp…
Exact Solution to a Dynamic SIR Model
Martin Bohner, Sabrina Streipert, Delfim F. M. Torres
We investigate an epidemic model based on Bailey's continuous differential system. In the continuous time domain, we extend the classical model to time-dependent coefficients and p…
Analysis of a SIRI epidemic model with distributed delay and relapse
Abdelhai Elazzouzi, Abdesslem Lamrani Alaoui, Mouhcine Tilioua +1
We investigate the global behaviour of a SIRI epidemic model with distributed delay and relapse. From the theory of functional differential equations with delay, we prove that the…
Solutions of systems with the Caputo-Fabrizio fractional delta derivative on time scales
Dorota Mozyrska, Delfim F. M. Torres, Malgorzata Wyrwas
Caputo-Fabrizio fractional delta derivatives on an arbitrary time scale are presented. When the time scale is chosen to be the set of real numbers, then the Caputo-Fabrizio fractio…
Structural derivatives on time scales
Benaoumeur Bayour, Delfim F. M. Torres
We introduce the notion of structural derivative on time scales. The new operator of differentiation unifies the concepts of fractal and fractional order derivative and is motivate…
New inequalities for -quasiconvex functions
Eze R. Nwaeze, Delfim F. M. Torres
The class of -quasiconvex functions was introduced in 2016. Here we establish novel inequalities of Ostrowski type for functions whose second derivative, in absolute value raise…
Some inequalities for interval-valued functions on time scales
Dafang Zhao, Guoju Ye, Wei Liu +1
We introduce the interval Darboux delta integral (shortly, the -integral) and the interval Riemann delta integral (shortly, the -integral) for interval-valued funct…
Variable order Mittag-Leffler fractional operators on isolated time scales and application to the calculus of variations
Thabet Abdeljawad, Raziye Mert, Delfim F. M. Torres
We introduce new fractional operators of variable order on isolated time scales with Mittag-Leffler kernels. This allows a general formulation of a class of fractional variational…
Existence of solution to a nonlocal conformable fractional thermistor problem
Moulay Rchid Sidi Ammi, Delfim F. M. Torres
We study a nonlocal thermistor problem for fractional derivatives in the conformable sense. Classical Schauder's fixed point theorem is used to derive the existence of a tube solut…
Generalized Fractional Operators on Time Scales with Application to Dynamic Equations
Kheira Mekhalfi, Delfim F. M. Torres
We introduce more general concepts of Riemann-Liouville fractional integral and derivative on time scales, of a function with respect to another function. Sufficient conditions for…
Novel results on Hermite-Hadamard kind inequalities for -convex functions by means of -fractional integral operators
Eze R. Nwaeze, Delfim F. M. Torres
We establish new integral inequalities of Hermite-Hadamard type for the recent class of -convex functions. This is done via generalized -Riemann-Liouville fractional inte…
The fuzzy Henstock-Kurzweil delta integral on time scales
Dafang Zhao, Guoju Ye, Wei Liu +1
We investigate properties of the fuzzy Henstock-Kurzweil delta integral (shortly, FHK -integral) on time scales, and obtain two necessary and sufficient conditions for FHK -i…
Generalized weighted Ostrowski and Ostrowski-Grüss type inequalities on time scales via a parameter function
Seth Kermausuor, Eze R. Nwaeze, Delfim F. M. Torres
We prove generalized weighted Ostrowski and Ostrowski--Grüss type inequalities on time scales via a parameter function. In particular, our result extends a result of Dragomir and B…
Existence of positive solutions to a discrete fractional boundary value problem and corresponding Lyapunov-type inequalities
Amar Chidouh, Delfim F. M. Torres
We prove existence of positive solutions to a boundary value problem depending on discrete fractional operators. Then, corresponding discrete fractional Lyapunov-type inequalities…
A Truly Conformable Calculus on Time Scales
Benaoumeur Bayour, Ahmed Hammoudi, Delfim F. M. Torres
We introduce the definition of conformable derivative on time scales and develop its calculus. Fundamental properties of the conformable derivative and integral on time scales are…
Existence theorems for a nonlinear second-order distributional differential equation
Wei Liu, Guoju Ye, Dafang Zhao +1
In this work, we are concerned with existence of solutions for a nonlinear second-order distributional differential equation, which contains measure differential equations and stoc…
Lyapunov-type inequality for a fractional boundary value problem with natural conditions
Assia Guezane-Lakoud, Rabah Khaldi, Delfim F. M. Torres
We derive a new Lyapunov type inequality for a boundary value problem involving both left Riemann--Liouville and right Caputo fractional derivatives in presence of natural conditio…
On the Henstock-Kurzweil Integral for Riesz-space-valued Functions on Time Scales
Xuexiao You, Dafang Zhao, Delfim F. M. Torres
We introduce and investigate the Henstock-Kurzweil (HK) integral for Riesz-space-valued functions on time scales. Some basic properties of the HK delta integral for Riesz-space-val…
On a Fractional Oscillator Equation with Natural Boundary Conditions
Assia Guezane-Lakoud, Rabah Khaldi, Delfim F. M. Torres
We prove existence of solutions for a nonlinear fractional oscillator equation with both left Riemann-Liouville and right Caputo fractional derivatives subject to natural boundary…
Non-differentiable solutions for local fractional nonlinear Riccati differential equations
Xiao-Jun Yang, H. M. Srivastava, Delfim F. M. Torres +1
We investigate local fractional nonlinear Riccati differential equations (LFNRDE) by transforming them into local fractional linear ordinary differential equations. The case of LFN…
Chain rules and inequalities for the BHT fractional calculus on arbitrary time scales
Eze R. Nwaeze, Delfim F. M. Torres
We develop the Benkhettou-Hassani-Torres fractional (noninteger order) calculus on time scales by proving two chain rules for the -fractional derivative and five inequalities fo…