Initial Value Problem for Stochastic Hyprid Hadamard Fractional Differential Equation

Hyprid Hadamard

  • Mahmoud Mohammed Mostafa El-Borai Alexandria University
  • Wagdy G. El-sayed Alexandria University
  • A. A. Badr
  • Ahmed Tarek Sayed Alexandria University
Keywords: Stochastic analysis, Hadamard-type fractional dierential equa- tions, Hyprid fractional dierential equations, Stochastic dierential equations

Abstract

In this paper, we discuss the existence of solutions for a stochastic initial value problem of Hyprid fractional dierential equations of Hadamard type given by 

                         Capture_jam.PNG

where HD is the Hadamard fractional derivative, Capturejam2.PNGCapturejam3.PNGand Capture111.PNGis the Hadamard fractional integral and Capture.PNGbe such that Capture222.PNGare investigated. The fractional calculus and stochastic analysis techniques are used to obtain the required results. 

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Author Biographies

Mahmoud Mohammed Mostafa El-Borai, Alexandria University

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

Wagdy G. El-sayed, Alexandria University

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

A. A. Badr

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

Ahmed Tarek Sayed, Alexandria University

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

Published
2019-02-28
How to Cite
El-Borai, M. M. M., El-sayed, W. G., Badr, A. A., & Sayed, A. T. (2019). Initial Value Problem for Stochastic Hyprid Hadamard Fractional Differential Equation. JOURNAL OF ADVANCES IN MATHEMATICS, 16, 8288-8296. https://doi.org/10.24297/jam.v16i0.8113
Section
Articles