Existence and Uniqueness of Mild Solution Where α ∈ (1,2) for Fuzzy Fractional Evolution Equations with Uncertainty

Ramsha Shafqat; Azmat Ullah Khan Niazi; Mdi Begum Jeelani; Nadiyah Hussain Alharthi

doi:10.3390/fractalfract6020065

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Existence and Uniqueness of Mild Solution Where α ∈ (1,2) for Fuzzy Fractional Evolution Equations with Uncertainty

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Existence and Uniqueness of Mild Solution Where α ∈ (1,2) for Fuzzy Fractional Evolution Equations with Uncertainty

Ramsha Shafqat, Azmat Ullah Khan Niazi, Mdi Begum Jeelani and Nadiyah Hussain Alharthi

Fractal and fractional, Vol.6(2), p.65

01/01/2022

DOI: https://doi.org/10.3390/fractalfract6020065

Abstract

This paper concerns with the existence and uniqueness of fuzzy fractional evolution equation with uncertainty involves function of form cDαx(t)=f(t,x(t),Dβx(t)),Iαx(0)=x0,x′(0)=x1, where 1<α<2,0<β<1. After determining the equivalent integral form of solution we establish existence and uniqueness by using Rogers conditions, Kooi type conditions and Krasnoselskii-Krein type conditions. In addition, various numerical solutions have been presented to ensure that the main result is true and effective. Finally, a few examples which express fuzzy fractional evolution equations are shown.

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Title: Existence and Uniqueness of Mild Solution Where α ∈ (1,2) for Fuzzy Fractional Evolution Equations with Uncertainty
Creators - without role: Ramsha Shafqat - University of Lahore
Azmat Ullah Khan Niazi - University of Sargodha
Mdi Begum Jeelani - Imam Mohammad ibn Saud Islamic University
Nadiyah Hussain Alharthi - Imam Mohammad ibn Saud Islamic University
Publication Details: Fractal and fractional, Vol.6(2), p.65
Identifiers: 9916191708331
Academic Unit: Imam Mohammad Ibn Saud Islamic University (IMSIU)
Language: English
Resource Type: Journal article