A natural extension of Mittag-Leffler function associated with a triple infinite series

Huseynov, Ismail T.; Ahmadovay, Arzu; Ojo, Gbenga O.; Mahmudov, Nazım I.

doi:10.48550/arxiv.2011.03999

Cited by 3 publications

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“…53 Extensions to two or three parameters are well known and thoroughly studied in textbooks such as Gorenflo et al 46 Extensions to two or several variables have been studied more recently. 8,[54][55][56][57] Definition 2.5 ( 53 ). The classical Mittag-Leffler function is defined by…”

Section: Preliminary Conceptmentioning

confidence: 99%

On a study of Sobolev‐type fractional functional evolution equations

Huseynov

Ahmadova

Mahmudov

2022

Math Methods in App Sciences

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Sobolev-type fractional functional evolution equations have many applications in the modeling of many physical processes. Therefore, we investigate the existence of mild solutions for fractional-order time-delay evolution equation of Sobolev type with multiorders in a Banach space with the help of two various methods. First, we study abstract problem by assuming the existence and compactness of E −1 and introduce a closed-form representation of a mild solution via a newly defined delayed Mittag-Leffler-type function which is generated by nonpermutable and permutable linear-bounded operators. Our second method is based on the theory of Sobolev-type delayed resolvent families generated by the pair (A, E) and a subordination principle, and in this case, any restrictive assumptions are not required on E. Furthermore, we derive an exact analytical representation of solutions for multidimensional fractional functional dynamical systems with nonpermutable and permutable matrices. As an example, the Sobolev-type delayed wave equation with a damping term is provided to illustrate the applications of the abstract results.

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Section: Preliminary Conceptmentioning

confidence: 99%

On a study of Sobolev‐type fractional functional evolution equations

Huseynov

Ahmadova

Mahmudov

2022

Math Methods in App Sciences

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“…Notice that from the viewpoint of fractional calculus and applications, the readers may find interesting more detailed studies of the bivariate (n = 2) [40] and trivariate (n = 3) [41] cases.…”

Section: Constant Coefficientsmentioning

confidence: 99%

Explicit solutions for linear variable–coefficient fractional differential equations with respect to functions

Restrepo

Ruzhansky

Сураган

2021

Applied Mathematics and Computation

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“…Extensions to two, three and multi-parameters are well known and thoroughly studied in textbooks such as [26,31] which are involving single power series in one variable [32,33,34]. Extensions to two, three, or more variables, involving correspondingly double, triple, or multiple power series, have been studied more recently [18,35,36,37].…”

Section: Definition 25 ([8]mentioning

confidence: 99%

Fractional Leibniz integral rules for Riemann-Liouville and Caputo fractional derivatives and their applications

Huseynov,

Ahmadova,

Mahmudov

2020

Preprint

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In recent years, the theory for Leibniz integral rule in the fractional sense has not been able to get substantial development. As an urgent problem to be solved, we study a Leibniz integral rule for Riemann-Liouville and Caputo type differentiation operators with general fractional-order of n − 1 < α ≤ n, n ∈ N . A rule of fractional differentiation under integral sign with general order is necessary and applicable tool for verification by substitution for candidate solutions of inhomogeneous multi-term fractional differential equations. We derive explicit analytical solutions of generalized Bagley-Torvik equations in terms of recently defined bivariate Mittag-Leffler type functions that based on fractional Green's function method and verified solutions by substitution in accordance by applying the fractional Leibniz integral rule. Furthermore, we study an oscillator equation as a special case of differential equations with multi-orders via the Leibniz integral rule.

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A natural extension of Mittag-Leffler function associated with a triple infinite series

Cited by 3 publications

References 0 publications

On a study of Sobolev‐type fractional functional evolution equations

On a study of Sobolev‐type fractional functional evolution equations

Explicit solutions for linear variable–coefficient fractional differential equations with respect to functions

Fractional Leibniz integral rules for Riemann-Liouville and Caputo fractional derivatives and their applications

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