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Related papers: On Some Operators Involving Hadamard Derivatives

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In this paper, we introduce a new generalized class of analytic functions involving the Mittag-Leffler operator and Bazilevi\u{c} functions. We examine inclusion properties, radius problems and an application of the generalized…

Complex Variables · Mathematics 2021-09-29 Om Ahuja , Asena Çetinkaya , Naveen Kumar Jain

In this paper, we propose a solution of fractional logistic equation by using properties of Mittag-Leffler function.

Classical Analysis and ODEs · Mathematics 2017-02-21 Jignesh P. Chauhan , Ranjan K. Jana , Pratik V. Shah , Ajay K. Shukla

We establish a new natural extension of Mittag-Leffler function with three variables which is so called "trivariate Mittag-Leffler function". The trivariate Mittag-Leffler function can be expressed via complex integral representation by…

Classical Analysis and ODEs · Mathematics 2020-11-10 Ismail T. Huseynov , Arzu Ahmadovay , Gbenga O. Ojo , Nazim I. Mahmudov

The computation of the Mittag-Leffler (ML) function with matrix arguments, and some applications in fractional calculus, are discussed. In general the evaluation of a scalar function in matrix arguments may require the computation of…

Numerical Analysis · Mathematics 2019-12-03 Roberto Garrappa , Marina Popolizio

We study the new class of q-fractional integral operator. In the aid of iterated Cauchy integral approach to fractional integral operator, we applied t^pf(t) instead of f(t) in these integrals and with parameter p a new class of…

General Mathematics · Mathematics 2019-04-29 Mohammad Momenzadeh , Nazim Mahmudov

We define an analogue of the classical Mittag-Leffler function which is applied to two variables, and establish its basic properties. Using a corresponding single-variable function with fractional powers, we define an associated fractional…

Classical Analysis and ODEs · Mathematics 2021-05-03 Arran Fernandez , Cemaliye Kürt , Mehmet Ali Özarslan

There is no unified method to solve the fractional differential equation. The type of derivative here used in this paper is of Jumarie formulation, for the several differential equations studied. Here we develop an algorithm to solve the…

Classical Analysis and ODEs · Mathematics 2016-03-14 Uttam Ghosh , Srijan Sengupta , Susmita Sarkar , Shantanu Das

In this paper we consider a modified fractional Maxwell model based on the application of Hadamard-type fractional derivatives. The model is physically motivated by the fact that we can take into account at the same time memory effects and…

Analysis of PDEs · Mathematics 2022-09-07 Roberto Garra , Armando Consiglio , Francesco Mainardi

In this paper, we propose a delayed perturbation of Mittag-Leffler type matrix function, which is an extension of the classical Mittag-Leffler type matrix function and delayed Mittag-Leffler type matrix function. With the help of the…

Dynamical Systems · Mathematics 2020-01-08 N. I. Mahmudov

This paper aims to investigate properties associated with fractional integral operators involving the three-parameters Mittag-Leffler function in the kernels with respect to another function. We prove that the Cauchy problem and the…

Classical Analysis and ODEs · Mathematics 2020-07-13 D. S. Oliveira

A new type of an integrable mapping is presented. This map is equipped with fractional difference and possesses an exact solution, which can be regarded as a discrete analogue of the Mittag-Leffler function.

Exactly Solvable and Integrable Systems · Physics 2007-05-23 Atsushi Nagai

We show how a rescaling of fractional operators with bounded kernels may help circumvent their documented deficiencies, for example, the inconsistency at zero or the lack of inverse integral operator. On the other hand, we build a novel…

Probability · Mathematics 2024-11-18 Marc Jornet

A strong inspiration for studying Sobolev type fractional evolution equations comes from the fact that have been verified to be useful tools in the modeling of many physical processes. We introduce a novel technique for solving Sobolev type…

Analysis of PDEs · Mathematics 2021-02-23 Nazim I. Mahmudov , Arzu Ahmadova , Ismail T. Huseynov

Our aim in this report is to investigate the asymptotic behavior of Mittag-Leffler functions. We give some estimates involving the Mittag-Leffler functions and their derivatives.

Classical Analysis and ODEs · Mathematics 2017-09-22 H. T. Tuan

We provide a fast and simple method to solve fractional variational problems with dependence on Hadamard fractional derivatives. Using a relation between the Hadamard fractional operator and a sum involving integer-order derivatives, we…

Optimization and Control · Mathematics 2014-05-07 Ricardo Almeida , Nuno R. O. Bastos , Delfim F. M. Torres

The properties of Mittag-Leffler function is reviewed within the framework of an umbral formalism. We take advantage from the formal equivalence with the exponential function to define the relevant semigroup properties. We analyse the…

Mathematical Physics · Physics 2018-08-15 Giuseppe Dattoli , Katarzyna Gorska , Andrzej Horzela , Silvia Licciardi , Rosa Maria Pidatella

The Mittag-Leffler type functions arise naturally in the solution of fractional order integral and differential equations, especially in the investigations of the fractional generalization of the kinetic equation. This article introduces a…

Complex Variables · Mathematics 2026-05-25 Urvashi Purohit Sharma , Ritu Agarwal

We aim to introduce a new extension of Mittag-Leffler function via q-analogue and obtained their significant properties including integral representation, q-differentiation, q-Laplace transform, image formula under q-derivative operators.…

Classical Analysis and ODEs · Mathematics 2019-01-18 Raghib Nadeem , Mohd. Saif , Talha Usman , Abdul Hakim Khan

In this paper we consider the problem of estimation of oscillatory integrals with Mittag-Leffler functions in two variables. The generalisation is that we replace the exponential function with the Mittag-Leffler-type function, to study…

Classical Analysis and ODEs · Mathematics 2023-01-12 Isroil A. Ikromov , Michael Ruzhansky , Akbar R. Safarov

We introduce a new fractional derivative that generalizes the so-called alternative fractional derivative recently proposed by Katugampola. We denote this new differential operator by $\mathscr{D}_{M}^{\alpha,\beta }$, where the parameter…

Classical Analysis and ODEs · Mathematics 2017-08-18 J. Vanterler da C. Sousa , E. Capelas de Oliveira