scholarly journals Boundary value problems for impulsive multi-order Hadamard fractional differential equations

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Weera Yukunthorn ◽  
Suthep Suantai ◽  
Sotiris K Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Hadamard Fractional Differential Equations ◽  
Fractional Differential

Existence and uniqueness results for Riemann–Stieltjes integral boundary value problems of nonlinear implicit Hadamard fractional differential equations

2021 ◽  
Author(s):  
Mohamed I. Abbas
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Stieltjes Integral ◽  
Integral Boundary ◽  
Hadamard Fractional Differential Equations ◽  
Fractional Differential ◽  
Integral Boundary Value Problems

In this paper, we study the existence and uniqueness of solutions for Riemann–Stieltjes integral boundary value problems of nonlinear implicit Hadamard fractional differential equations. The investigation of the main results depends on Schauder’s fixed point theorem and Banach’s contraction principle. An illustrative example is given to show the applicability of theoretical results.

A wavelet method for solving Caputo–Hadamard fractional differential equation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Umer Saeed
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Fractional Integration ◽  
Operational Matrix ◽  
Operational Matrices ◽  
Content Type ◽  
Hadamard Fractional Differential Equations ◽  
Fractional Differential

PurposeThe purpose of the present work is to propose a wavelet method for the numerical solutions of Caputo–Hadamard fractional differential equations on any arbitrary interval.Design/methodology/approachThe author has modified the CAS wavelets (mCAS) and utilized it for the solution of Caputo–Hadamard fractional linear/nonlinear initial and boundary value problems. The author has derived and constructed the new operational matrices for the mCAS wavelets. Furthermore, The author has also proposed a method which is the combination of mCAS wavelets and quasilinearization technique for the solution of nonlinear Caputo–Hadamard fractional differential equations.FindingsThe author has proved the orthonormality of the mCAS wavelets. The author has constructed the mCAS wavelets matrix, mCAS wavelets operational matrix of Hadamard fractional integration of arbitrary order and mCAS wavelets operational matrix of Hadamard fractional integration for Caputo–Hadamard fractional boundary value problems. These operational matrices are used to make the calculations fast. Furthermore, the author works out on the error analysis for the method. The author presented the procedure of implementation for both Caputo–Hadamard fractional initial and boundary value problems. Numerical simulation is provided to illustrate the reliability and accuracy of the method.Originality/valueMany scientist, physician and engineers can take the benefit of the presented method for the simulation of their linear/nonlinear Caputo–Hadamard fractional differential models. To the best of the author’s knowledge, the present work has never been proposed and implemented for linear/nonlinear Caputo–Hadamard fractional differential equations.

scholarly journals Separated Boundary Value Problems of Sequential Caputo and Hadamard Fractional Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Jessada Tariboon ◽  
Asawathep Cuntavepanit ◽  
Sotiris K. Ntouyas ◽  
Woraphak Nithiarayaphaks
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Uniqueness Of Solutions ◽  
Hadamard Fractional Differential Equations ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

In this paper, we discuss the existence and uniqueness of solutions for new classes of separated boundary value problems of Caputo-Hadamard and Hadamard-Caputo sequential fractional differential equations by using standard fixed point theorems. We demonstrate the application of the obtained results with the aid of examples.

scholarly journals Solutions for Integral Boundary Value Problems of Nonlinear Hadamard Fractional Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Keyu Zhang ◽  
Jianguo Wang ◽  
Wenjie Ma
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Existence Theorems ◽  
Boundary Value ◽  
Nontrivial Solutions ◽  
Integral Boundary ◽  
Hadamard Fractional Differential Equations ◽  
Fractional Differential ◽  
Integral Boundary Value Problems

In this paper using fixed point methods we establish some existence theorems of positive (nontrivial) solutions for integral boundary value problems of nonlinear Hadamard fractional differential equations.

scholarly journals On the Boundary Value Problems of Hadamard Fractional Differential Equations of Variable Order via Kuratowski MNC Technique

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1134
Author(s):  
Ahmed Refice ◽  
Mohammed Said Souid ◽  
Ivanka Stamova
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Measure Of Noncompactness ◽  
Boundary Value ◽  
Variable Order ◽  
Kuratowski Measure Of Noncompactness ◽  
Hadamard Fractional Differential Equations ◽  
Fractional Differential ◽  
The Stability

In this manuscript, we examine both the existence and the stability of solutions of the boundary value problems of Hadamard-type fractional differential equations of variable order. New outcomes are obtained in this paper based on the Darbo’s fixed point theorem (DFPT) combined with Kuratowski measure of noncompactness (KMNC). We construct an example to illustrate the validity of the observed results.

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