Results 31 to 40 of about 1,581 (158)

A matrix approach to multi-term fractional differential equations using two new diffusive representations for the Caputo fractional derivative [PDF]

AUT Journal of Mathematics and Computing
In the last decade, there has been a surge of interest in application of fractional calculus in various areas such as, mathematics, physics, engineering, mechanics and etc.
Hassan Khosravian-Arab, Mehdi Dehghan
doaj   +1 more source

About fractional integrals in the space of locally integrable functions

Journal of Mathematical Analysis and Applications, 1992
The authors show that the largest ``natural'' function space, where the Riemann-Liouville fractional integral operator \[ J^ \alpha f(x)={1\over{\Gamma(\alpha)}} \int_ 0^ x (x-t)^{\alpha-1} f(t)dt \] and differential operator \[ D^ \alpha f(x)={1 \over{\Gamma(1-\alpha)}} {d \over dx} \int_ 0^ x (x-t)^{-\alpha} f(t)dt ...
Martinez, Celso, Sanz, Miguel, Martinez, Ma Dolores   +2 more
openaire   +1 more source

Some Hermite–Hadamard type inequalities for generalized h-preinvex function via local fractional integrals and their applications

Advances in Difference Equations, 2020
The concept of generalized h-preinvex function on real linear fractal sets R β $R^{\beta }$ ( 0 < β ≤ 1 $0 < \beta \le 1$ ) is introduced, which extends generalized preinvex, generalized s-preinvex, generalized Godunova–Levin preinvex, and generalized P ...
Wenbing Sun
doaj   +1 more source

Certain Analytic Formulas Linked to Locally Fractional Differential and Integral Operators

Journal of Function Spaces, 2022
The present investigation is aimed at defining different classes of analytic functions and conformable differential operators in view of the concept of locally fractional differential and integral operators. We present a novel generalized class of analytic functions, which we call it locally fractional analytic functions in the open unit disk.
Ibtisam Aldawish, Rabha W. Ibrahim
openaire   +3 more sources

Iterative Convergence with Banach Space Valued Functions in Abstract Fractional Calculus

Annals of the West University of Timisoara: Mathematics and Computer Science, 2017
The goal of this paper is to present a semi-local convergence analysis for some iterative methods under generalized conditions. The operator is only assumed to be continuous and its domain is open. Applications are suggested including Banach space valued
Anastassiou George A., Argyros Ioannis K.   +1 more
doaj   +1 more source

ON A PROBLEM FOR THE LOADED MIXED TYPE EQUATION WITH FRACTIONAL DERIVATIVE

Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2016
An existence and an uniqueness of solution of local boundary value problem with discontinuous matching condition for the loaded parabolic-hyperbolic equation involving the Caputo fractional derivative and Riemann-Liouville integrals have been ...
Abdullaev, O.K.
doaj   +1 more source

On a Class of Partial Differential Equations and Their Solution via Local Fractional Integrals and Derivatives

Fractal and Fractional, 2022
This article investigates the local fractional generalized Kadomtsev–Petviashvili equation and the local fractional Kadomtsev–Petviashvili-modified equal width equation.
Mohammad Abdelhadi, Sharifah E. Alhazmi, Shrideh Al-Omari   +2 more
doaj   +1 more source

Local Fractional Integral Hölder-Type Inequalities and Some Related Results

Fractal and Fractional, 2022
This paper is devoted to establishing some functional generalizations of Hölder and reverse Hölder’s inequalities with local fractional integral introduced by Yang. Then, based on the obtained results, we derive some related inequalities including local fractional integral Minkowski-type and Dresher-type inequalities, which are some extensions of ...
Guangsheng Chen, Jiansuo Liang, Hari M. Srivastava, Chao Lv   +3 more
openaire   +2 more sources

Local fractional Newton’s inequalities involving generalized harmonic convex functions

Advances in Difference Equations, 2020
A new auxiliary result based on a three step quadratic kernel utilizing the concepts of local fractional calculus is obtained. Using this new auxiliary result we have several new Newton type inequalities whose power q of local fractional derivative in ...
Sabah Iftikhar, Samet Erden, Poom Kumam, Muhammad Uzair Awan   +3 more
doaj   +1 more source

Rough Fractional Integral Operators on Local Morrey Spaces

Journal of Physics: Conference Series, 2019
We prove the boundedness of rough fractional integral operator on local Morrey spaces for radial functions. We consider three ways of estimation of the operator to obtain our result.
Daniel Salim, Wono Setya Budhi, Yudi Soeharyadi   +2 more
openaire   +1 more source