A new exploration on existence of fractional neutral integro- differential equations in the concept of Atangana–Baleanu derivative

Logeswari, K.; Ravichandran, C.

doi:10.1016/j.physa.2019.123454

Cited by 53 publications

(28 citation statements)

References 27 publications

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“…Any traditional discussions indicate that literature on this topic may infer that the concept of F -contraction is a typical generalization of the Banach contraction principle as a consequence of the uniqueness. For a extensive study on fixed points, F -contraction and fractionals the reader may refer [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] , [29] , [30] , [31] , [32] , [33] , [34] .…”

Section: Results On Fractional Models Of 2019-ncovmentioning

confidence: 99%

Applying fixed point methods and fractional operators in the modelling of novel coronavirus 2019-nCoV/SARS-CoV-2

Panda¹

2020

Results in Physics

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Section: Results On Fractional Models Of 2019-ncovmentioning

confidence: 99%

Applying fixed point methods and fractional operators in the modelling of novel coronavirus 2019-nCoV/SARS-CoV-2

Panda¹

2020

Results in Physics

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“…Recently, many authors are proved and illustrated that, the model having hereditary and genetic consequences are effectively illustrated with the aid of fractional calculus [25–48]. Particularly, we the aid of new fractional derivative we can effectively model and examine various real models, specifically those related to epidemic models.…”

Section: Mathematical Formulation and Analysismentioning

confidence: 99%

A mathematical analysis of ongoing outbreakCOVID‐19 in India through nonsingular derivative

Safare¹,

Betageri²,

Prakasha

et al. 2020

Numerical Methods Partial

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Throughout the globe, mankind is in vastly infected situations due to a cruel and destructive virus called coronavirus (COVID‐19). The pivotal aim of the present investigation is to analyze and examine the evolution of COVID‐19 in India with the available data in two cases first from the beginning to 31st March and beginning to 23rd April in order to show its exponential growth in the crucial period. The present situation in India with respect to confirmed, active, recovered and deaths cases have been illustrated with the aid of available data. The species of novel virus and its stages of growth with respect some essential points are presented. The exponential growth of projected virus by the day‐to‐day base is captured in two‐dimensional plots to predict its developments and identify the needs to control its spread on mankind. Moreover, the SEIR model is considered to present some interesting consequences about COVID‐19 within the frame of fractional calculus. A newly proposed technique called q‐Homotopy analysis transform method (q‐HATM) is hired to find the solution for the nonlinear system portraying projected model and also presented the existence and uniqueness of the obtained results with help of fixed point theory. The behavior has been captured with respect to fractional order and time. The present study exemplifies the importance of fractional operator and efficiency of the projected algorithm.

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“…The existence solution of integrodifferential equations has been studied by several researchers, their different views, see previous works. [36][37][38][39][40][41][42][43][44][45] Consider the following functional integrodifferential equation:…”

Section: General Functional Integrodifferential Equationmentioning

confidence: 99%

Existence of solutions for some functional integrodifferential equations with nonlocal conditions

Munusamy¹,

Ravichandran²,

Nisar

et al. 2020

Math Methods in App Sciences

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In this paper, we discuss the existence of mild solution of functional inte grodifferential equation with nonlocal conditions. To establish this results by using the resolvent operator theory and Sadovskii-Krasnosel'skii type of fixed point theorem and to show the usefulness and the applicability of our results to a broad class of functional integrodifferential equations, an example is given to illustrate the theory.

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A new exploration on existence of fractional neutral integro- differential equations in the concept of Atangana–Baleanu derivative

Cited by 53 publications

References 27 publications

Applying fixed point methods and fractional operators in the modelling of novel coronavirus 2019-nCoV/SARS-CoV-2

Applying fixed point methods and fractional operators in the modelling of novel coronavirus 2019-nCoV/SARS-CoV-2

A mathematical analysis of ongoing outbreakCOVID‐19 in India through nonsingular derivative

Existence of solutions for some functional integrodifferential equations with nonlocal conditions

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