Existence and Uniqueness of Abstract Stochastic Fractional-Order Differential Equation

Authors

  • Mahmoud Mohammed Mostafa El-Borai Alexandria University
  • A. Tarek S.A. Alexandria University

DOI:

https://doi.org/10.24297/jam.v16i0.8097

Keywords:

Stochastic Differential Equations, Fractional Order, Existance and uniqueness theorems, Abstract Differential Equations

Abstract

In this paper, the existence and uniqueness about the solution for a class of abstract stochastic fractional-order differential equations

                                         Capture_new1.PNG

where Capture_new2.PNG in and Capture_new31.PNG are given functions, are investigated, where the fractional derivative is described in Caputo sense. The fractional calculus, stochastic analysis techniques and the standard $Picard's$ iteration method are used to obtain the required.

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Author Biographies

Mahmoud Mohammed Mostafa El-Borai, Alexandria University

Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt

A. Tarek S.A., Alexandria University

Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt

Published

2019-01-31

How to Cite

El-Borai, M. M. M., & S.A., A. T. (2019). Existence and Uniqueness of Abstract Stochastic Fractional-Order Differential Equation. JOURNAL OF ADVANCES IN MATHEMATICS, 16, 8280-8287. https://doi.org/10.24297/jam.v16i0.8097

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Section

Articles