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Some Theorems on Cauchy Problem for Nonlinear Fractional Differential Equations with Positive Constant Coefficient

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Abstract

In this paper, we consider a Cauchy problem for nonlinear fractional differential equation with constant coefficient \(\lambda >0\) of the type: \({^c}{D}^{\alpha }x(t)=\lambda x(t)+f(t,x(t))\) with \(x(0)=x_{0}.\) The aim of this paper is to investigate the existence and interval of existence of solutions, uniqueness, continuous dependence of solutions on initial conditions, estimates on solutions and continuous dependence on parameters and functions involved in the equations. Finally, one illustrative example is given to demonstrate the theoretical results.

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Authors and Affiliations

  1. Department of Mathematics, Kisan Veer Mahavidyalaya, Wai, Maharashtra, 412803, India

    Shivaji Tate

  2. Department of Mathematics, Karmaveer Bhaurao Patil College, Urun-Islampur, Maharashtra, 415409, India

    H. T. Dinde

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  1. Shivaji Tate
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  2. H. T. Dinde
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Correspondence to Shivaji Tate.

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Tate, S., Dinde, H.T. Some Theorems on Cauchy Problem for Nonlinear Fractional Differential Equations with Positive Constant Coefficient. Mediterr. J. Math. 14, 72 (2017). https://doi.org/10.1007/s00009-017-0886-x

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  • DOI: https://doi.org/10.1007/s00009-017-0886-x

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