At present, inequalities have reached an outstanding theoretical and applied development they are the methodological base of many mathematical processes. In particular, Hermite– Hadamard inequality has received considerable attention. this paper, we prove some new results related to Hermite–Hadamard via symmetric non-conformable integral operators.

In this paper we present an extension of Fractional Laplace Transform in the framework non-conformable local fractional derivative. Its main properties are studied and it is applied to resolution differential equations.

This Special Issue of the scientific journal Axioms, entitled “Recent Advances in Fractional Calculus”, is dedicated to one most dynamic areas mathematical sciences today [...]

This article explores the mechanical analysis of a unified chaotic system and matrix projective synchronization (MPS). The sufficient conditions to achieve MPS have derived. mechanics been examined in contrast with Kolmogorov system, Euler equation, Hamiltonian function. Casimir energy function is also introduced analyze dynamics. has transformed into type decomposed four types torques: inertial, internal, dissipation, external torque. In order view behind different particular cases...

We introduce a definition of generalized conformable derivative order α > 0 (where this parameter does not need to be integer), with which we overcome some deficiencies known local derivatives, or not.This allows us compute fractional derivatives functions defined on any open set the real line (and just positive halfline).Moreover, extend classical results context derivatives.Also, obtain for case 1.

This study undertakes a comparative analysis of the non conformable and fractional derivatives alongside Riemann-Liouville Caputo derivatives. It examines their efficacy in solving ordinary differential equations explores applications physics through numerical simulations. The findings suggest that derivative emerges as promising substitute for conformable, within range order $\alpha $ where $1/2 < \alpha 1$.

In this note, we review the latest qualitative results, referring to Li\'enard Equation, in framework of non-conformable, generalized and fractional differential operators.

This article discusses the existence of positive solutions to Sturm–Liouville boundary value problems for Riemann–Liouville nabla fractional difference equations. The results obtained here shall generalize existing ones. We provide a few examples illustrate applicability established results.

In this study, some inequalities of Hermite-Hadamard type for integrals arising in conformable fractional calculus are presented. fact, the obtained not only valid those calculus, but more general as well. Numerous known versions recovered special cases. We also illustrate our findings via applications to modified Bessel functions, means, and midpoint approximations.

This work presents new versions of the Hermite-Hadamard Inequality, for (m−F)-convex functions, defined on fractal sets Rς ( 0 ς ≤ 1). So, we show some results twice differentiable functions using local fractional calculus, as well definitions. We will construct these integral inequality generalized H¨older-integral and power mean inequality. Furthermore, present inequalities midpoint trapezoid formulas in a novel type calculus. The conclusions this paper are substantial advancements...

Abstract In this paper, we have established some generalized inequalities of Hermite–Hadamard–Fejér type for integrals. The results obtained are applied fractional integrals various and therefore contain previous reported in the literature.

In this paper, we present a general definition of generalized integral operator which contains as particular cases, many the well-known, fractional and integer order integrals.

In this paper, we introduce the Ω-derivative, which generalizes classical concept of derivative. Main properties new derivative are revised. We also study Ω-differential equations and some its applications.

In the article, new versions of integral inequalities Milne type are derived for pℎ, q-convex modified functions second on fractal sets.Based a generalized local fractional weighted operator, an identity is established as foundation subsequently obtained inequalities.Throughout our study, we certain results known in literature, which include particular cases findings.

In this work we present numerical results of classical Li\'{e}nard--type systems in a very general context, since consider several types derivatives (integer order and fractional order, global local). Additionally made theoretical-methodological observations. En este trabajo presentamos resultados num´ericos de sistemas tipo Li´enard en un contexto muy ya que consideramos varios tipos dederivadas (de orden entero y fraccionario, globales locales). Adicionalmente hacemos observaciones te...

In this paper, we use a conformable fractional derivative G T α , with kernel ( t ) = e − 1 in order to study the differential equation associated logistic growth model. As practical application, estimate of models, by solving an inverse problem involving real data. same direction, show feasibility our approach respect Ordinary, Khalil et al and Caputo approaches.

In this communication, using a generalized conformable differential operator, simulation of the well-known Newton’s law cooling is made. particular, we use t1−α, e(1−α)t and non-conformable t−α kernels. The analytical solution for each kernel given in terms order derivative 0<α≤1. Then, method inverse problem solving, Bayesian estimation with real temperature data to calculate parameters interest, applied. It shown that these approaches have an advantage respect ordinary derivatives.