Bitsadze–Samarskii type problem for the integro-differential diffusion–wave equation on the Heisenberg group

Ruzhansky, Michael; Tokmagambetov, Niyaz; Torebek, Berikbol T.

doi:10.1080/10652469.2019.1652823

Cited by 7 publications

(2 citation statements)

References 23 publications

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“…A similar problem for a multi-term fractional differential equation with the Caputo derivative was studied in [Gad18]. For more works related to this topic, we refer to the authors' papers [KMR18,RTT20a,RTT20b].…”

Section: Introductionmentioning

confidence: 99%

Initial, inner and inner-boundary problems for a fractional differential equation

Karimov,

Ruzhansky,

Tokmagambetov

2020

Preprint

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While it is known that one can consider the Cauchy problem for evolution equations with Caputo derivatives, the situation for the initial value problems for the Riemann-Liouville derivatives is less understood. In this paper we propose new type initial, inner and inner-boundary value problems for fractional differential equations with the Riemann-Liouville derivatives. The results on the existence and uniqueness are proved, and conditions on the solvability are found. The wellposedness of the new type initial, inner and inner-boundary conditions are also discussed. Moreover, we give explicit formulas for the solutions. As an application fractional partial differential equations for general positive operators are studied. Contents 1. Introduction 1 2. Cauchy type problems 4 2.1. Generalized initial (Cauchy) problem 5 2.2. Partial differential equations with the Cauchy type data 9 3. Inner value problem 12 3.1. Partial differential equations with the non-local Cauchy type data 14 4. Inner-boundary value problem 15 4.1. Inner-boundary value problem for time-fractional partial differential equations 16 References 17

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Section: Introductionmentioning

confidence: 99%

Initial, inner and inner-boundary problems for a fractional differential equation

Karimov,

Ruzhansky,

Tokmagambetov

2020

Preprint

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show abstract

“…The Oldroyd-B fluid is one of the most important classes for dilute solutions of polymers. We also note that integro-differential diffusion equations of type (1.1) were studied in [3,4,9,10,19,22].…”

Section: Introduction and Statement Of Problemmentioning

confidence: 99%