A novel approach to find exact solutions of fractional evolution equations with non-singular kernel derivative

2021 ◽  
Vol 152 ◽  
pp. 111367
Author(s):  
M.S. Hashemi
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Singular Kernel ◽  
Fractional Evolution Equations ◽  
Novel Approach

scholarly journals A Novel Analytical Technique to Obtain Kink Solutions for Higher Order Nonlinear Fractional Evolution Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Qazi Mahmood Ul Hassan ◽  
Jamshad Ahmad ◽  
Muhammad Shakeel
Keyword(s):  
Differential Equation ◽  
Exact Solutions ◽  
Fractional Derivatives ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Fractional Evolution Equations ◽  
Analytical Technique ◽  
Fractional Complex Transform ◽  
Fifth Order

We use the fractional derivatives in Caputo’s sense to construct exact solutions to fractional fifth order nonlinear evolution equations. A generalized fractional complex transform is appropriately used to convert this equation to ordinary differential equation which subsequently resulted in a number of exact solutions.

Application of a Homogeneous Balance Method to Exact Solutions of Nonlinear Fractional Evolution Equations

2014 ◽  
Vol 9 (2) ◽  
Author(s):  
H. Jafari ◽  
H. Tajadodi ◽  
D. Baleanu
Keyword(s):  
Exact Solutions ◽  
Fractional Derivatives ◽  
Evolution Equations ◽  
Telegraph Equation ◽  
Fisher Equation ◽  
Fractional Evolution Equations ◽  
Liouville Derivative ◽  
Nonlinear Telegraph Equation ◽  
Homogeneous Balance Method ◽  
Homogeneous Balance

The fractional Fan subequation method of the fractional Riccati equation is applied to construct the exact solutions of some nonlinear fractional evolution equations. In this paper, a powerful algorithm is developed for the exact solutions of the modified equal width equation, the Fisher equation, the nonlinear Telegraph equation, and the Cahn–Allen equation of fractional order. Fractional derivatives are described in the sense of the modified Riemann–Liouville derivative. Some relevant examples are investigated.

scholarly journals Multidimensional van der Corput-Type estimates involving Mittag-Leffler functions

2020 ◽  
Vol 23 (6) ◽  
pp. 1663-1677
Author(s):  
Michael Ruzhansky ◽  
Berikbol T. Torebek
Keyword(s):  
Cauchy Problem ◽  
Exponential Function ◽  
Evolution Equations ◽  
Oscillatory Integrals ◽  
Schrödinger Equations ◽  
Fractional Evolution Equations ◽  
Type Function ◽  
Fractional Schrödinger Equations ◽  
The Cauchy Problem ◽  
Klein Gordon

Abstract The paper is devoted to study multidimensional van der Corput-type estimates for the intergrals involving Mittag-Leffler functions. The generalisation is that we replace the exponential function with the Mittag-Leffler-type function, to study multidimensional oscillatory integrals appearing in the analysis of time-fractional evolution equations. More specifically, we study two types of integrals with functions E α, β (i λ ϕ(x)), x ∈ ℝ N and E α, β (i α λ ϕ(x)), x ∈ ℝ N for the various range of α and β. Several generalisations of the van der Corput-type estimates are proved. As an application of the above results, the Cauchy problem for the multidimensional time-fractional Klein-Gordon and time-fractional Schrödinger equations are considered.

scholarly journals Study of Hilfer fractional evolution equations by the properties of controllability and stability

2021 ◽  
Vol 60 (4) ◽  
pp. 3741-3749
Author(s):  
Pallavi Bedi ◽  
Anoop Kumar ◽  
Thabet Abdeljawad ◽  
Aziz Khan
Keyword(s):  
Evolution Equations ◽  
Fractional Evolution Equations

scholarly journals A study on controllability of impulsive fractional evolution equations via resolvent operators

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Haide Gou ◽  
Yongxiang Li
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Resolvent Operator ◽  
Evolution Equations ◽  
Validity Study ◽  
Resolvent Operators ◽  
Fractional Evolution Equations ◽  
Mönch Fixed Point Theorem ◽  
Alpha Beta

AbstractIn this article, we study the controllability for impulsive fractional integro-differential evolution equation in a Banach space. The discussions are based on the Mönch fixed point theorem as well as the theory of fractional calculus and the $(\alpha ,\beta )$ ( α , β ) -resolvent operator, we concern with the term $u'(\cdot )$ u ′ ( ⋅ ) and finding a control v such that the mild solution satisfies $u(b)=u_{b}$ u ( b ) = u b and $u'(b)=u'_{b}$ u ′ ( b ) = u b ′ . Finally, we present an application to support the validity study.

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