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Generalizations of some Integral Inequalities for Fractional Integrals [PDF]

Annales Mathematicae Silesianae, 2018
Abstract In this paper we give generalizations of the Hadamard-type inequalities for fractional integrals. As special cases we derive several Hadamard type inequalities.
Farid Ghulam, ur Rehman Atiq
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Convergence analysis for the fractional decomposition method applied to class of nonlinear fractional Fredholm integro-differential equation

Journal of Algorithms & Computational Technology, 2023
For scientists conducting research, fractional integral differential equation analysis is crucial. Therefore, in this study, we investigate analysis utilizing a novel method called the fractional decomposition method, which is applicable to fractional ...
Mahmoud S Rawashdeh, Hala Abedalqader, Nazek A Obeidat   +2 more
doaj   +1 more source

General Non-Local Continuum Mechanics: Derivation of Balance Equations

Mathematics, 2022
In this paper, mechanics of continuum with general form of nonlocality in space and time is considered. Some basic concepts of nonlocal continuum mechanics are discussed. General fractional calculus (GFC) and general fractional vector calculus (GFVC) are
Vasily E. Tarasov
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Certain generalized fractional integral inequalities

AIMS Mathematics, 2020
الهدف الرئيسي من هذه المقالة هو إنشاء بعض التفاوتات التكاملية الجزئية المعممة من خلال استخدام مشغل التكامل الجزئي ماريتشيف- سايغو- القاعدة (MSM). بعض الفئات الجديدة من المتباينات التكاملية الكسرية المعممة لفئة من n (n $ $\mathbb{N}$) الدوال الإيجابية المستمرة والمتناقصة على [a, b] باستخدام عامل التكامل الكسري MSM المشتق أيضًا.
Kottakkaran Sooppy Nisar, Gauhar Rahman, Aftab Khan, Asifa Tassaddiq, M. S. Abouzaid   +4 more
openaire   +5 more sources

On positive solutions of a system of equations generated by Hadamard fractional operators

Advances in Difference Equations, 2020
This paper is devoted to studying some systems of quadratic differential and integral equations with Hadamard-type fractional order integral operators.
Amira M. Abdalla, Hussein A. H. Salem, Kinga Cichoń   +2 more
doaj   +1 more source

General Fractional Calculus Operators of Distributed Order

Axioms, 2023
In this paper, two types of general fractional derivatives of distributed order and a corresponding fractional integral of distributed type are defined, and their basic properties are investigated.
Mohammed Al-Refai, Yuri Luchko
doaj   +1 more source

Levi-Civita cylinders with fractional angular deficit [PDF]

, 2011
The angular deficit factor in the Levi-Civita vacuum metric has been parametrized using a Riemann-Liouville fractional integral. This introduces a new parameter into the general relativistic cylinder description, the fractional index {\alpha}.
Bicak J., Butzer P. L., E. N. Glass, Holvorcem P. R., J. P. Krisch, Levi-Civita T., Mainardi F., Oldham K. B., Podlubny I., Poisson E., Samko S. G.   +10 more
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New generalized Pólya–Szegö and Čebyšev type inequalities with general kernel and measure

Advances in Difference Equations, 2020
It is always attractive and motivating to acquire the generalizations of known results. In this article, we introduce a new class C ( h ) $\mathfrak{C(h)}$ of functions which can be represented in a form of integral transforms involving general kernel ...
S. Iqbal, M. Samraiz, Thabet Abdeljawad, Kottakkaran Sooppy Nisar, G. Rahman, M. Adil Khan   +5 more
doaj   +1 more source

ITERATED 𝐺-FRACTIONAL VECTOR REPRESENTATION FORMULAE AND INEQUALITIES FOR BANACH SPACE VALUED FUNCTIONS

Проблемы анализа, 2020
Here we present very general iterated fractional Bochner integral representation formulae for Banach space valued functions. Based on these we derive generalized and iterated left and right: fractional Poincar´e type inequalities, fractional Opial type ...
George A. Anastassiou
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Existence of Solutions to a System of Riemann-Liouville Fractional Differential Equations with Coupled Riemann-Stieltjes Integrals Boundary Conditions

Fractal and Fractional, 2022
A general system of fractional differential equations with coupled fractional Stieltjes integrals and a Riemann–Liouville fractional integral in boundary conditions is studied in the context of pattern formation.
Yuan Ma, Dehong Ji
doaj   +1 more source