Ahmad M Ahmad

King Fahd University of Petroleum and Minerals, Mathematics and Statistics, Graduate Student

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Mario Cavani

Universidad de Oriente

teodoro lara

Universidad de Los Andes (Venezuela)

Vladimir Kozlov

Albert Luo

Southern Illinois University Edwardsville

abdelmajid siai

Dan Burghelea

Ohio State University

John M Rassias

National & Kapodistrian University of Athens

Başak Karpuz

Manuel Valdes

Universitat de Barcelona

Lonnie J Mott

Fayetteville Technical Community College

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Papers by Ahmad M Ahmad

ASYMPTOTIC POWER TYPE BEHAVIOR OF SOLUTIONS TO A NONLINEAR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATION

by Ahmad M Ahmad and Khaled Furati

Ahmad, Ahmad M., Khaled M. Furati, and Nasser-Eddine Tatar. "Asymptotic power type behavior of solutions to a nonlinear fractional integro-differential equation." Electronic Journal of Differential Equations 2017.134 (2017): 1-16., 2017

This article concerns a general fractional differential equation of order between 1 and 2. We con... more This article concerns a general fractional differential equation of order between 1 and 2. We consider the cases where the nonlinear term contains or does not contain other (lower order) fractional derivatives (of Riemann-Liouville type). Moreover, the nonlinearity involves also a nonlinear non-local in time term. The case where this non-local term has a singular kernel is treated as well. It is proved, in all these situations, that solutions approach power type functions at infinity.

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$Research paper thumbnail of On the nonexistence of global solutions for a class of fractional integro-differential problems$

On the nonexistence of global solutions for a class of fractional integro-differential problems

by Ahmad M Ahmad and Khaled Furati

We study the nonexistence of (nontrivial) global solutions for a class of fractional integro-diff... more We study the nonexistence of (nontrivial) global solutions for a class of fractional integro-differential problems in an appropriate underlying space. Integral conditions on the kernel, and for some degrees of the involved parameters, ensuring the nonexistence of global solutions are determined. Unlike the existing results, the source term considered is, in general, a convolution and therefore nonlocal in time. The class of problems we consider includes problems with sources that are polynomials and fractional integrals of polynomials in the state as special cases. Singular kernels illustrating interesting cases in applications are provided and discussed. Our results are obtained by considering a weak formulation of the problem with an appropriate test function and several appropriate estimations.

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Research Article Symmetries, Conservation Laws, and Wave Equation on the Milne Metric

by Ahmad M Ahmad and Ashfaque Bokhari

Noether symmetries provide conservation laws that are admitted by Lagrangians representing physic... more Noether symmetries provide conservation laws that are admitted by Lagrangians representing physical systems. For partial differential equation possessing Lagrangians these symmetries are obtained by the invariance of the corresponding action integral. In this paper we provide a systematic procedure for determining Noether symmetries and conserved vectors for a Lagrangian constructed from a Lorentzian metric of interest in mathematical physics. For completeness, we give Lie point symmetries and conservation laws admitted by the wave equation on this Lorentzian metric.

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ASYMPTOTIC POWER TYPE BEHAVIOR OF SOLUTIONS TO A NONLINEAR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATION

by Ahmad M Ahmad and Khaled Furati

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$Research paper thumbnail of On the nonexistence of global solutions for a class of fractional integro-differential problems$

On the nonexistence of global solutions for a class of fractional integro-differential problems

by Ahmad M Ahmad and Khaled Furati

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Research Article Symmetries, Conservation Laws, and Wave Equation on the Milne Metric

by Ahmad M Ahmad and Ashfaque Bokhari

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Ahmad M Ahmad

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