Analytical solution for the generalized time-fractional telegraph equation

Chaurasia, V. B. L.; Dubey, Ravi Shanker

doi:10.7153/fdc-03-02

Cited by 18 publications

(10 citation statements)

References 11 publications

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“…Many types of problems can be defined by the help of fractional‐order integration and fractional‐order differentiation. These include, but are not limited to, stochastic processes, blood glucose insulin model, Brownian motion, fractional oxygen diffusion problem, control theory, viscoelasticity, fractals and nonlocal phenomena, time fractional telegraph equation, space‐time fractional Fokker‐Plank equation, fractional LC‐circuit models, fractional Klein‐Gordon equations, heat conduction, image and signal processing, control theory, and controllability of fractional delay dynamical systems (see, for details, other studies()).…”

Section: An Introductory Overview Of Fractional Calculusmentioning

confidence: 99%

A study of the fractional‐order mathematical model of diabetes and its resulting complications

Srivástava

Dubey

Jain

2019

Math Methods in App Sciences

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Diabetes is a worldwide problem that affects one of every 11 persons nowadays. The IDF Diabetes Atlas (Eighth edition, 2017) states that approximately 415 million people in the world are living with the disease and that this number will rise to 629 million by the year 2045. It is a very serious problem of the world. A major part of the world population is affected by this disease and its resulting complications. In this paper, we propose to investigate a fractional-order model of diabetes and its resulting complications. The mathematical model's parameters define the population of diabetic patients and those who are diabetic with complications at a given time t. We have also discussed the existence, uniqueness, and stability of the fractional-order model, which we consider here. We make use of the homotopy decomposition method (HDM) in order to solve the problem. KEYWORDSdiabetes and its resulting complications, existence, fractional calculus, fractional-order modeling, homotopy decomposition method (HDM), uniqueness and stability

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Section: An Introductory Overview Of Fractional Calculusmentioning

confidence: 99%

A study of the fractional‐order mathematical model of diabetes and its resulting complications

Srivástava

Dubey

Jain

2019

Math Methods in App Sciences

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“…Fractional telegrapher's equation, containing the fractional derivatives of orders ∈ (0, 2) and ∈ (0, 1), instead of the second and first order partial derivatives in (1.1), is considered in [3,28]. Multi-term fractional telegrapher's equation, considered in [8], contain terms of fractional derivatives of orders , with ∈ {1, . .…”

Section: Introduction and Model Formulationmentioning

confidence: 99%

Fractional telegrapher’s equation as a consequence of Cattaneo’s heat conduction law generalization

Zorica

Cveticanin

2018

Theor appl mech (Belgr)

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Fractional telegrapher's equation is reinterpreted in the setting of heat conduction phenomena and reobtained by considering the energy balance equation and fractional Cattaneo heat conduction law, generalized by taking into account the history of temperature gradient as well. Using the Laplace transform method, fractional telegrapher's equation is solved on semi-bounded domain for the zero initial condition and solution is obtained as a convolution of forcing temperature on the boundary and impulse response. Some features of such obtained solution are examined.

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“…Mitchell studied the accurate application of the integral method [19]. For more details see [2,5,6,8,9,13,15,18,21].…”

Section: Introductionmentioning

confidence: 99%

“…After this research, the mathematicians faced some complex problems of real world. To solve them mathematicians introduced fractional derivative (see [2,6,8,15,21]). The concept of fractional calculus has great importance in many branches and is also important for modeling real world problem (see [5,9,13]).…”

Section: Introductionmentioning

confidence: 99%