# Numerical Solution for Solving Fractional Diﬀerential Equations using Shifted Chebyshev Wavelet

Mohamed Elarabi Benattia , Belghaba Kacem

In this paper, we are interested to develop a numerical method based on the Chebyshev wavelets for solving fractional order diﬀerential equations (FDEs). As a result of the presentation of Chebyshev wavelets, we highlight the operational matrix of the fractional order derivative through wavelet-polynomial ...

# Bernoulli Operational Matrix of Fractional Derivative for Solution of Fractional Diﬀerential Equations

Rachid Belgacem , Ahmed Bokhari , Abdessamad Amir

The aim of this paper is to present a numerical method based on Bernoulli polynomials for numerical solutions of fractional diﬀerential equations(FDEs). The Bernoulli operational matrix of fractional derivatives is derived and used together with tau and collocation methods to reduce the FDEs to a ...

# On the Study of Nonlinear Fractional Diﬀerential Equations on Unbounded Interval

Ahmed Hallaci , Hamid Boulares , Muhammet Kurulay

By the means of the variation of constants formula and some analytical skills, we use Banach contraction principle to investigate in this paper an uniqueness and existence of unbounded solution for nonlinear diﬀerential equations of fractional orders in weighted Banach space. At last, we present an illustrative ...

# Existence and Ulam stability of solutions for Caputo-Hadamard fractional differential equations

In this paper, we study the existence of solutions for fractional differential equations with the Caputo-Hadamard fractional derivative of order 2 (1, 2]. The uniqueness result is proved via Banach&rsquo;s contraction mapping principle and the existence results are established by using the Schauder&rsquo;s ...

# Stability for Pantograph Fractional Differential Equations

Hamid Boulares

In this manuscript, we studied some sufficient condition for the asymptotically stable of the zero solution of pantograph Caputo fractional differential equations of order (1 &lt; &lt; 2). In a weighted Banach space, we used Krasnoselskii&rsquo;s fixed point theorem to derive new reIn this manuscript, ...